Verfügbarkeit: Representation theory and complex analysis

Representation theory and complex analysis: lectures given at the CIME summer school held in Venice, Italy, June 10 - 17, 2004

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Format:	Buch
Sprache:	English
Veröffentlicht:	Berlin [u.a.] Springer [u.a.] 2008
Schriftenreihe:	Lecture notes in mathematics 1931
Schlagworte:	Harmonic analysis > Congresses Representations of groups > Congresses Funktionentheorie Darstellungstheorie Konferenzschrift > 2004 > Venedig
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XII, 380 S. graph. Darst. 235 mm x 155 mm
ISBN:	9783540768913 3540768912

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245	1	0	\|a Representation theory and complex analysis \|b lectures given at the CIME summer school held in Venice, Italy, June 10 - 17, 2004 \|c Michael Cowling ... Ed.: Enrico Casadio Tarabusi ...
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Datensatz im Suchindex

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adam_text	Contents Applications of Representation Theory to Harmonic Analysis of Lie Groups (and Vice Versa) Michael Cowling ................................................ 1 1 Basic Facts of Harmonic Analysis on Semisimple Groups and Symmetric Spaces ........................................ 2 1.1 Structure of Semisimple Lie Algebras ....................... 2 1.2 Decompositions of Semisimple Lie Groups ................... 4 1.3 Parabolic Subgroups ...................................... 5 1.4 Spaces of Homogeneous Functions on G ..................... 6 1.5 The Plancherel Formula ................................... 8 2 The Equations of Mathematical Physics on Symmetric Spaces ...... 10 2.1 Spherical Analysis on Symmetric Spaces .....................■ 10 2.2 Harmonic Analysis on Semisimple Groups and Symmetric Spaces .................................................. 12 2.3 Regularity of the Lapí ace-Beltrami Operator ................ 16 2.4 Approaches to the Heat Equation .......................... 18 2.5 Estimates for the Heat and Laplace Equations ............... 18 2.6 Approaches to the Wave and Schrödinger Equations .......... 20 2.7 Further Results .......................................... 21 3 The Vanishing of Matrix Coefficients ............................ 22 3.1 Some Examples in Representation Theory ................... 22 3.2 Matrix Coefficients of Representations of Semisimple Groups. .. 24 3.3 The Kunze-Stein Phenomenon ............................. 27 3.4 Property Τ .............................................. 28 3.5 The Generalised Ramanujan-Selberg Property ............... 29 4 More General Semisimple Groups .............................. 31 4.1 Graph Theory and its Riemannian Connection ............... 31 4.2 Cayley Graphs ........................................... 32 4.3 An Example Involving Cayley Graphs ....................... 33 4.4 The Field of p-adic Numbers ............................... 34 4.5 Lattices in Vector Spaces over Local Fields .................. 35 4.6 Adèles .................................................. 36 VIII Contents 4.7 Further Results .......................................... 37 5 Carnot-Carathéodory Geometry and Group Representations ....... 38 5.1 A Decomposition for Real Rank One Groups ................. 38 5.2 The Conformai Group of the Sphere in Rn .................. 38 5.3 The Groups SU(l,ra + 1) and Sp(l,n+ 1)................... 41 References ..................................................... 46 Ramifications of the Geometric Langlands Program Edward Frenkel ................................................ 51 Introduction .................................................... 51 1 The Unramified Global Langlands Correspondence ................ 56 2 Classical Local Langlands Correspondence ....................... 61 2.1 Langlands Parameters .................................... 61 2.2 The Local Langlands Correspondence for GLn ............... 62 2.3 Generalization to Other Reductive Groups ................... 63 3 Geometric Local Langlands Correspondence over С ............... 64 3.1 Geometric Langlands Parameters ........................... 64 3.2 Representations of the Loop Group ......................... 65 3.3 Prom Functions to Sheaves ................................ 66 3.4 A Toy Model ............................................ 68 3.5 Back to Loop Groups ..................................... 70 4 Center and Opers ............................................ 71 4.1 Center of an Abelian Category ............................. 71 4.2 Opers ................................................... 73 4.3 Canonical Representatives ................................. 75 4.4 Description of the Center .................................. 76 5 Opers vs. Local Systems ....................................... 77 6 Harish-Chandra Categories .................................... 81 6.1 Spaces of IT-Invariant Vectors .............................. 81 6.2 Equivariant Modules ...................................... 82 6.3 Categorical Hecke Algebras ................................ 83 7 Local Langlands Correspondence: Unramified Case ............... 85 7.1 Unramified Representations of G{F) ........................ 85 7.2 Unramified Categories gK(,-Modules ......................... 87 7.3 Categories of G[[i]]-Equivariant Modules .................... 88 7.4 The Action of the Spherical Hecke Algebra .................. 90 7.5 Categories of Representations and D-Modules ................ 92 7.6 Equivalences Between Categories of Modules ................. 96 7.7 Generalization to other Dominant Integral Weights ........... 98 8 Local Langlands Correspondence: Tamely Ramified Case .......... 99 8.1 Tamely Ramified Representations .......................... 99 8.2 Categories Admitting (gKc,I) Harish-Chandra Modules ....... 103 8.3 Conjectural Description of the Categories of QKc,I) Harish-Chandra Modules .................................. 105 8.4 Connection between the Classical and the Geometric Settings .. 109 Contents IX 8.5 Evidence for the Conjecture ............................... 115 9 Ramified Global Langlands Correspondence ...................... 117 9.1 The Classical Setting ..................................... 117 9.2 The Unramified Case, Revisited ............................ 120 9.3 Classical Langlands Correspondence with Ramification ........ 122 9.4 Geometric Langlands Correspondence in the Tamely Ramified Case .................................................... 122 9.5 Connections with Regular Singularities ...................... 126 9.6 Irregular Connections ..................................... 130 References ..................................................... 132 Equivariant Derived Category and Representation of Real Semisimple Lie Groups Masaki Kashiwara .............................................. 137 1 Introduction ................................................. 137 1.1 Harish-Chandra Correspondence ........................... 138 1.2 Beilinson-Bernstein Correspondence ........................ 140 1.3 Riemann-Hilbert Correspondence ........................... 141 1.4 Matsuki Correspondence .................................. 142 1.5 Construction of Representations of Gk ...................... 143 1.6 Integral Transforms ....................................... 146 1.7 Commutativity of Fig. 1 .................................. 147 1.8 Example ................................................ 148 1.9 Organization of the Note .................................. 151 2 Derived Categories of Quasi-abelian Categories ................... 152 2.1 Quasi-abelian Categories .................................. 152 2.2 Derived Categories ....................................... 154 2.3 ¿-Structure .............................................. 156 3 Quasi-equivariant .D-Modules .................................. 158 3.1 Definition ............................................... 158 3.2 Derived Categories ....................................... 162 3.3 Sumihiro s Result ........................................ 163 3.4 Pull-back Functors ....................................... 167 3.5 Push-forward Functors .................................... 168 3.6 External and Internal Tensor Products ...................... 170 3.7 Semi-outer Hom .......................................... 171 3.8 Relations of Push-forward and Pull-back Functors ............ 172 3.9 Flag Manifold Case ....................................... 175 4 Equivariant Derived Category .................................. 176 4.1 Introduction ............................................. 176 4.2 Sheaf Case .............................................. 176 4.3 Induction Functor ........................................ 179 4.4 Constructible Sheaves ..................................... 179 4.5 D-module Case .......................................... 180 4.6 Equivariant Riemann-Hilbert Correspondence ................ 181 X Contents 5 Holomorphic Solution Spaces .................................. 182 5.1 Introduction ............................................. 182 5.2 Countable Sheaves ....................................... 183 5.3 C^-Solutions ............................................ 185 5.4 Definition of RHomtop .................................... 186 5.5 DFN Version ............................................ 189 5.6 Punctorial Properties of RHomtop .......................... 190 5.7 Relation with the de Rham Functor ........................ 192 6 Whitney Functor ............................................. 194 6.1 Whitney Functor ......................................... 194 6.2 The Functor RHorn*^. ( ·, · S> ffx^) ....................... 195 6.3 Elliptic Case ............................................. 196 7 Twisted Sheaves .............................................. 197 7.1 Twisting Data ........................................... 197 7.2 Twisted Sheaf ........................................... 198 7.3 Morphism of Twisting Data ............................... 199 7.4 Tensor Product .......................................... 200 7.5 Inverse and Direct Images ................................. 200 7.6 Twisted Modules ......................................... 201 7.7 Equivariant Twisting Data ................................ 201 7.8 Character Local System ................................... 202 7.9 Twisted Equivariance ..................................... 202 7.10 Twisting Data Associated with Principal Bundles ............ 203 7.11 Twisting (D-module Case) ................................ 204 7.12 Ring of Twisted Differential Operators ...................... 205 7.13 Equivariance of Twisted Sheaves and Twisted D-modules ...... 207 7.14 Riemann-Hilbert Correspondence ........................... 207 8 Integral Transforms ........................................... 208 8.1 Convolutions ............................................ 208 8.2 Integral Transform Formula ............................... 209 9 Application to the Representation Theory ....................... 210 9.1 Notations ............................................... 210 9.2 Beilinson-Bernstein Correspondence ........................ 212 9.3 Quasi-equivariant D-modules on the Symmetric Space ........ 214 9.4 Matsuki Correspondence .................................. 216 9.5 Construction of Representations ............................ 217 9.6 Integral Transformation Formula ........................... 219 10 Vanishing Theorems .......................................... 221 10.1 Preliminary .............................................. 221 10.2 Calculation (I) ........................................... 222 10.3 Calculation (II) .......................................... 224 10.4 Vanishing Theorem ....................................... 226 References ..................................................... 229 List of Notations ............................................. 231 Index ......................................................... 233 Contents XI Amenability and Margulis Super-Rigidity Alain Valette................................................... 235 1 Introduction ................................................. 235 2 Amenability for Locally Compact Groups ........................ 236 2.1 Definition, Examples, and First Characterizations ............ 236 2.2 Stability Properties ....................................... 239 2.3 Lattices in Locally Compact Groups ........................ 240 2.4 Reiter s Property (Ρχ) .................................... 241 2.5 Reiter s Property (P2) .................................... 242 2.6 Amenability in Riemannian Geometry ...................... 244 3 Measurable Ergodic Theory .................................... 244 3.1 Definitions and Examples ................................. 244 3.2 Moore s Ergodicity Theorem ............................... 247 3.3 The Howe-Moore Vanishing Theorem ....................... 249 4 Margulis Super-rigidity Theorem ............................... 252 4.1 Statement ............................................... 252 4.2 Mostów Rigidity ......................................... 252 4.3 Ideas to Prove Super-rigidity, fc = R ........................ 253 4.4 Proof of Furstenberg s Proposition 4.1 - Use of Amenability. ... 255 4.5 Margulis Arithmeticity Theorem ........................... 256 References ..................................................... 257 Unitary Representations and Complex Analysis David A. Yogan, Jr............................................. 259 1 Introduction ................................................. 259 2 Compact Groups and the Borei- Weil Theorem ................... 264 3 Examples for SL(2,~R) ........................................ 272 4 Harish-Chandra Modules and Globalization ...................... 274 5 Real Parabolic Induction and the Globalization Functors .......... 284 6 Examples of Complex Homogeneous Spaces ...................... 294 7 Dolbeault Cohomology and Maximal Globalizations ............... 302 8 Compact Supports and Minimal Globalizations ................... 318 9 Invariant Bilinear Forms and Maps between Representations ....... 327 10 Open Questions .............................................. 341 References ..................................................... 343 Quantum Computing and Entanglement for Mathematicians Nolan R. Wallach............................................... 345 1 The Basics .................................................. 346 1.1 Basic Quantum Mechanics ................................. 346 1.2 Bits .................................................... 348 1.3 Qubits .................................................. 349 References ..................................................... 350 2 Quantum Algorithms ......................................... 351 2.1 Quantum Parallelism ..................................... 351 XII Contents 2.2 The Tensor Product Structure of n-qubit Space .............. 352 2.3 Grover s Algorithm ....................................... 353 2.4 The Quantum Fourier Transform ........................... 354 References ..................................................... 355 3 Factorization and Error Correction ............................. 355 3.1 The Complexity of the Quantum Fourier Transform .......... 356 3.2 Reduction of Factorization to Period Search ................. 359 3.3 Error Correction ......................................... 360 References ..................................................... 362 4 Entanglement ................................................ 362 4.1 Measures of Entanglement ................................. 363 4.2 Three Qubits ............................................ 365 4.3 Measures of Entanglement for Two and Three Qubits ......... 367 References ..................................................... 368 5 Four and More Qubits ........................................ 369 5.1 Four Qubits ............................................. 369 5.2 Some Hubert Series of Measures of Entanglement ............ 374 5.3 A Measure of Entanglement for η Qubits .................... 374 References ..................................................... 376
adam_txt	Contents Applications of Representation Theory to Harmonic Analysis of Lie Groups (and Vice Versa) Michael Cowling . 1 1 Basic Facts of Harmonic Analysis on Semisimple Groups and Symmetric Spaces . 2 1.1 Structure of Semisimple Lie Algebras . 2 1.2 Decompositions of Semisimple Lie Groups . 4 1.3 Parabolic Subgroups . 5 1.4 Spaces of Homogeneous Functions on G . 6 1.5 The Plancherel Formula . 8 2 The Equations of Mathematical Physics on Symmetric Spaces . 10 2.1 Spherical Analysis on Symmetric Spaces .■ 10 2.2 Harmonic Analysis on Semisimple Groups and Symmetric Spaces . 12 2.3 Regularity of the Lapí ace-Beltrami Operator . 16 2.4 Approaches to the Heat Equation . 18 2.5 Estimates for the Heat and Laplace Equations . 18 2.6 Approaches to the Wave and Schrödinger Equations . 20 2.7 Further Results . 21 3 The Vanishing of Matrix Coefficients . 22 3.1 Some Examples in Representation Theory . 22 3.2 Matrix Coefficients of Representations of Semisimple Groups. . 24 3.3 The Kunze-Stein Phenomenon . 27 3.4 Property Τ . 28 3.5 The Generalised Ramanujan-Selberg Property . 29 4 More General Semisimple Groups . 31 4.1 Graph Theory and its Riemannian Connection . 31 4.2 Cayley Graphs . 32 4.3 An Example Involving Cayley Graphs . 33 4.4 The Field of p-adic Numbers . 34 4.5 Lattices in Vector Spaces over Local Fields . 35 4.6 Adèles . 36 VIII Contents 4.7 Further Results . 37 5 Carnot-Carathéodory Geometry and Group Representations . 38 5.1 A Decomposition for Real Rank One Groups . 38 5.2 The Conformai Group of the Sphere in Rn . 38 5.3 The Groups SU(l,ra + 1) and Sp(l,n+ 1). 41 References . 46 Ramifications of the Geometric Langlands Program Edward Frenkel . 51 Introduction . 51 1 The Unramified Global Langlands Correspondence . 56 2 Classical Local Langlands Correspondence . 61 2.1 Langlands Parameters . 61 2.2 The Local Langlands Correspondence for GLn . 62 2.3 Generalization to Other Reductive Groups . 63 3 Geometric Local Langlands Correspondence over С . 64 3.1 Geometric Langlands Parameters . 64 3.2 Representations of the Loop Group . 65 3.3 Prom Functions to Sheaves . 66 3.4 A Toy Model . 68 3.5 Back to Loop Groups . 70 4 Center and Opers . 71 4.1 Center of an Abelian Category . 71 4.2 Opers . 73 4.3 Canonical Representatives . 75 4.4 Description of the Center . 76 5 Opers vs. Local Systems . 77 6 Harish-Chandra Categories . 81 6.1 Spaces of IT-Invariant Vectors . 81 6.2 Equivariant Modules . 82 6.3 Categorical Hecke Algebras . 83 7 Local Langlands Correspondence: Unramified Case . 85 7.1 Unramified Representations of G{F) . 85 7.2 Unramified Categories gK(,-Modules . 87 7.3 Categories of G[[i]]-Equivariant Modules . 88 7.4 The Action of the Spherical Hecke Algebra . 90 7.5 Categories of Representations and D-Modules . 92 7.6 Equivalences Between Categories of Modules . 96 7.7 Generalization to other Dominant Integral Weights . 98 8 Local Langlands Correspondence: Tamely Ramified Case . 99 8.1 Tamely Ramified Representations . 99 8.2 Categories Admitting (gKc,I) Harish-Chandra Modules . 103 8.3 Conjectural Description of the Categories of QKc,I) Harish-Chandra Modules . 105 8.4 Connection between the Classical and the Geometric Settings . 109 Contents IX 8.5 Evidence for the Conjecture . 115 9 Ramified Global Langlands Correspondence . 117 9.1 The Classical Setting . 117 9.2 The Unramified Case, Revisited . 120 9.3 Classical Langlands Correspondence with Ramification . 122 9.4 Geometric Langlands Correspondence in the Tamely Ramified Case . 122 9.5 Connections with Regular Singularities . 126 9.6 Irregular Connections . 130 References . 132 Equivariant Derived Category and Representation of Real Semisimple Lie Groups Masaki Kashiwara . 137 1 Introduction . 137 1.1 Harish-Chandra Correspondence . 138 1.2 Beilinson-Bernstein Correspondence . 140 1.3 Riemann-Hilbert Correspondence . 141 1.4 Matsuki Correspondence . 142 1.5 Construction of Representations of Gk . 143 1.6 Integral Transforms . 146 1.7 Commutativity of Fig. 1 . 147 1.8 Example . 148 1.9 Organization of the Note . 151 2 Derived Categories of Quasi-abelian Categories . 152 2.1 Quasi-abelian Categories . 152 2.2 Derived Categories . 154 2.3 ¿-Structure . 156 3 Quasi-equivariant .D-Modules . 158 3.1 Definition . 158 3.2 Derived Categories . 162 3.3 Sumihiro's Result . 163 3.4 Pull-back Functors . 167 3.5 Push-forward Functors . 168 3.6 External and Internal Tensor Products . 170 3.7 Semi-outer Hom . 171 3.8 Relations of Push-forward and Pull-back Functors . 172 3.9 Flag Manifold Case . 175 4 Equivariant Derived Category . 176 4.1 Introduction . 176 4.2 Sheaf Case . 176 4.3 Induction Functor . 179 4.4 Constructible Sheaves . 179 4.5 D-module Case . 180 4.6 Equivariant Riemann-Hilbert Correspondence . 181 X Contents 5 Holomorphic Solution Spaces . 182 5.1 Introduction . 182 5.2 Countable Sheaves . 183 5.3 C^-Solutions . 185 5.4 Definition of RHomtop . 186 5.5 DFN Version . 189 5.6 Punctorial Properties of RHomtop . 190 5.7 Relation with the de Rham Functor . 192 6 Whitney Functor . 194 6.1 Whitney Functor . 194 6.2 The Functor RHorn*^. ( ·, · S> ffx^) . 195 6.3 Elliptic Case . 196 7 Twisted Sheaves . 197 7.1 Twisting Data . 197 7.2 Twisted Sheaf . 198 7.3 Morphism of Twisting Data . 199 7.4 Tensor Product . 200 7.5 Inverse and Direct Images . 200 7.6 Twisted Modules . 201 7.7 Equivariant Twisting Data . 201 7.8 Character Local System . 202 7.9 Twisted Equivariance . 202 7.10 Twisting Data Associated with Principal Bundles . 203 7.11 Twisting (D-module Case) . 204 7.12 Ring of Twisted Differential Operators . 205 7.13 Equivariance of Twisted Sheaves and Twisted D-modules . 207 7.14 Riemann-Hilbert Correspondence . 207 8 Integral Transforms . 208 8.1 Convolutions . 208 8.2 Integral Transform Formula . 209 9 Application to the Representation Theory . 210 9.1 Notations . 210 9.2 Beilinson-Bernstein Correspondence . 212 9.3 Quasi-equivariant D-modules on the Symmetric Space . 214 9.4 Matsuki Correspondence . 216 9.5 Construction of Representations . 217 9.6 Integral Transformation Formula . 219 10 Vanishing Theorems . 221 10.1 Preliminary . 221 10.2 Calculation (I) . 222 10.3 Calculation (II) . 224 10.4 Vanishing Theorem . 226 References . 229 List of Notations . 231 Index . 233 Contents XI Amenability and Margulis Super-Rigidity Alain Valette. 235 1 Introduction . 235 2 Amenability for Locally Compact Groups . 236 2.1 Definition, Examples, and First Characterizations . 236 2.2 Stability Properties . 239 2.3 Lattices in Locally Compact Groups . 240 2.4 Reiter's Property (Ρχ) . 241 2.5 Reiter's Property (P2) . 242 2.6 Amenability in Riemannian Geometry . 244 3 Measurable Ergodic Theory . 244 3.1 Definitions and Examples . 244 3.2 Moore's Ergodicity Theorem . 247 3.3 The Howe-Moore Vanishing Theorem . 249 4 Margulis' Super-rigidity Theorem . 252 4.1 Statement . 252 4.2 Mostów Rigidity . 252 4.3 Ideas to Prove Super-rigidity, fc = R . 253 4.4 Proof of Furstenberg's Proposition 4.1 - Use of Amenability. . 255 4.5 Margulis' Arithmeticity Theorem . 256 References . 257 Unitary Representations and Complex Analysis David A. Yogan, Jr. 259 1 Introduction . 259 2 Compact Groups and the Borei- Weil Theorem . 264 3 Examples for SL(2,~R) . 272 4 Harish-Chandra Modules and Globalization . 274 5 Real Parabolic Induction and the Globalization Functors . 284 6 Examples of Complex Homogeneous Spaces . 294 7 Dolbeault Cohomology and Maximal Globalizations . 302 8 Compact Supports and Minimal Globalizations . 318 9 Invariant Bilinear Forms and Maps between Representations . 327 10 Open Questions . 341 References . 343 Quantum Computing and Entanglement for Mathematicians Nolan R. Wallach. 345 1 The Basics . 346 1.1 Basic Quantum Mechanics . 346 1.2 Bits . 348 1.3 Qubits . 349 References . 350 2 Quantum Algorithms . 351 2.1 Quantum Parallelism . 351 XII Contents 2.2 The Tensor Product Structure of n-qubit Space . 352 2.3 Grover's Algorithm . 353 2.4 The Quantum Fourier Transform . 354 References . 355 3 Factorization and Error Correction . 355 3.1 The Complexity of the Quantum Fourier Transform . 356 3.2 Reduction of Factorization to Period Search . 359 3.3 Error Correction . 360 References . 362 4 Entanglement . 362 4.1 Measures of Entanglement . 363 4.2 Three Qubits . 365 4.3 Measures of Entanglement for Two and Three Qubits . 367 References . 368 5 Four and More Qubits . 369 5.1 Four Qubits . 369 5.2 Some Hubert Series of Measures of Entanglement . 374 5.3 A Measure of Entanglement for η Qubits . 374 References . 376
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indexdate	2024-07-09T21:13:05Z
institution	BVB
isbn	9783540768913 3540768912
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-016393577
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physical	XII, 380 S. graph. Darst. 235 mm x 155 mm
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series2	Lecture notes in mathematics
spelling	Representation theory and complex analysis lectures given at the CIME summer school held in Venice, Italy, June 10 - 17, 2004 Michael Cowling ... Ed.: Enrico Casadio Tarabusi ... Berlin [u.a.] Springer [u.a.] 2008 XII, 380 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1931 Harmonic analysis Congresses Representations of groups Congresses Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2004 Venedig gnd-content Darstellungstheorie (DE-588)4148816-7 s Funktionentheorie (DE-588)4018935-1 s DE-604 Cowling, Michael Sonstige oth Casadio Tarabusi, Enrico Sonstige oth Lecture notes in mathematics 1931 (DE-604)BV000676446 1931 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016393577&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Representation theory and complex analysis lectures given at the CIME summer school held in Venice, Italy, June 10 - 17, 2004 Lecture notes in mathematics Harmonic analysis Congresses Representations of groups Congresses Funktionentheorie (DE-588)4018935-1 gnd Darstellungstheorie (DE-588)4148816-7 gnd
subject_GND	(DE-588)4018935-1 (DE-588)4148816-7 (DE-588)1071861417
title	Representation theory and complex analysis lectures given at the CIME summer school held in Venice, Italy, June 10 - 17, 2004
title_auth	Representation theory and complex analysis lectures given at the CIME summer school held in Venice, Italy, June 10 - 17, 2004
title_exact_search	Representation theory and complex analysis lectures given at the CIME summer school held in Venice, Italy, June 10 - 17, 2004
title_exact_search_txtP	Representation theory and complex analysis lectures given at the CIME summer school held in Venice, Italy, June 10 - 17, 2004
title_full	Representation theory and complex analysis lectures given at the CIME summer school held in Venice, Italy, June 10 - 17, 2004 Michael Cowling ... Ed.: Enrico Casadio Tarabusi ...
title_fullStr	Representation theory and complex analysis lectures given at the CIME summer school held in Venice, Italy, June 10 - 17, 2004 Michael Cowling ... Ed.: Enrico Casadio Tarabusi ...
title_full_unstemmed	Representation theory and complex analysis lectures given at the CIME summer school held in Venice, Italy, June 10 - 17, 2004 Michael Cowling ... Ed.: Enrico Casadio Tarabusi ...
title_short	Representation theory and complex analysis
title_sort	representation theory and complex analysis lectures given at the cime summer school held in venice italy june 10 17 2004
title_sub	lectures given at the CIME summer school held in Venice, Italy, June 10 - 17, 2004
topic	Harmonic analysis Congresses Representations of groups Congresses Funktionentheorie (DE-588)4018935-1 gnd Darstellungstheorie (DE-588)4148816-7 gnd
topic_facet	Harmonic analysis Congresses Representations of groups Congresses Funktionentheorie Darstellungstheorie Konferenzschrift 2004 Venedig
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016393577&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000676446
work_keys_str_mv	AT cowlingmichael representationtheoryandcomplexanalysislecturesgivenatthecimesummerschoolheldinveniceitalyjune10172004 AT casadiotarabusienrico representationtheoryandcomplexanalysislecturesgivenatthecimesummerschoolheldinveniceitalyjune10172004

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