The Schur lectures (1992):
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Ramat-Gan
Bar-Ilan Univ.
1995
|
| Series: | Israel Mathematical Conference: Israel Mathematical Conference proceedings
8 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Enth.: Perspectives on invariant theory / Roger Howe. Arithmetic quantum chaos / Peter Sarnak |
| Physical Description: | VII, 236 S. Ill., graph. Darst. |
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| 245 | 1 | 0 | |a The Schur lectures (1992) |c Ilya Piatetski-Shapiro ... ed. |
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| 300 | |a VII, 236 S. |b Ill., graph. Darst. | ||
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| 490 | 1 | |a Israel Mathematical Conference: Israel Mathematical Conference proceedings |v 8 | |
| 500 | |a Enth.: Perspectives on invariant theory / Roger Howe. Arithmetic quantum chaos / Peter Sarnak | ||
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| 650 | 4 | |a Complex manifolds | |
| 650 | 4 | |a Hamiltonian systems | |
| 650 | 4 | |a Invariants | |
| 650 | 4 | |a Quantum chaos | |
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Record in the Search Index
| _version_ | 1804125362103255040 |
|---|---|
| adam_text | Table of Contents
Preface vji
Part I. Perspectives on Invariant Theory
Roger Howe
1. Basic theory 3
1.1. Highest weight theory 3
1.2. GLn and diagram notation 8
1.3. Multiplicity free actions 11
2. Multiplicity free actions and classical invariant theory: Case of GLn 15
2.1. (GLn,GLm) duality 15
2.2. First fundamental theorem for GLn, standard polynomial form 17
2.3. Operator commutant version of the FFT 20
2.4. Relation to Schur duality 21
2.5. Full isotypic decomposition of V{Vl ® (V)m) 26
2.6. The second fundamental theorem 29
2.7. (GLn, GLm) duality and the role of the Capelli identities 30
3. The FFT for the other classical groups 32
3.1. The action of GLn on symmetric matrices 32
3.2. Proof of Theorem 3.1 32
3.3. Complements to Theorem 3.1 33
3.4. FFT for On, standard polynomial version 34
3.5. Operator commutant and full isotypic decomposition for On 36
3.6. Structure of the harmonics 37
3.7. Geometry of the quotient mapping 40
3.8. Synopsis of results for Sp2n 44
V
vi TABLE OF CONTENTS
4. Skew symmetric multiplicity free actions 50
4.1. Skew (GLn, GLm) duality 50
4.2. The skew FFT for GLn 51
4.3. The FFT for isometry groups 53
4.4. A(5f2(C )) and A(A2(C )) 58
4.5. Skew multiplicity free actions, generalities 60
4.6. Classification of weight multiplicity free modules 62
4.7. Classification of skew multiplicity free modules 65
5. Examples
5.1. Classical symmetric spaces: cohomology and invariant differential
operators 69
5.2. Other first fundamental theorems 71
5.3. Covariants of subspaces 74
5.4. Branching laws 78
5.5. Abelian and Heisenberg nilradicals 91
5.6. The tensor product problem 95
5.7. Reciprocity laws and stability properties 115
Appendix 1. The symmetric space S2n/Dn 120
Appendix 2. Weyl algebra, Clifford algebra 123
Appendix 3. Varieties of isotropic subspaces 134
Appendix 4. Examples of skew duality 143
Appendix 5. Tables of skew multiplicity free actions 150
Appendix 6. Geometry of tensor products for SL3 168
References 178
Part II. Arithmetic Quantum Chaos
Peter Sarnak
1. Background 183
2. Report on numerical experiments 191
2.1. The stadium 191
2.2. Hyperbolic surfaces 195
2.3. Fine structure of the spectrum 206
3. Arithmetic manifolds 210
4. L functions 219
5. Outline of some proofs 226
6. Conclusion 233
References 234
|
| any_adam_object | 1 |
| author | Howe, Roger 1945- Sarnak, Peter 1953- |
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| author_facet | Howe, Roger 1945- Sarnak, Peter 1953- |
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| author_sort | Howe, Roger 1945- |
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| classification_rvk | SD 1992 |
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| dewey-full | 512.5 |
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512.5 |
| dewey-search | 512.5 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010873720 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:00:21Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007269663 |
| oclc_num | 35207734 |
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| owner | DE-355 DE-BY-UBR |
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| physical | VII, 236 S. Ill., graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Bar-Ilan Univ. |
| record_format | marc |
| series | Israel Mathematical Conference: Israel Mathematical Conference proceedings |
| series2 | Israel Mathematical Conference: Israel Mathematical Conference proceedings |
| spelling | The Schur lectures (1992) Ilya Piatetski-Shapiro ... ed. Ramat-Gan Bar-Ilan Univ. 1995 VII, 236 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Israel Mathematical Conference: Israel Mathematical Conference proceedings 8 Enth.: Perspectives on invariant theory / Roger Howe. Arithmetic quantum chaos / Peter Sarnak Schur, Issai 1875-1941 (DE-588)118795627 gnd rswk-swf Complex manifolds Hamiltonian systems Invariants Quantum chaos Invariantentheorie (DE-588)4162209-1 gnd rswk-swf Quantenchaos (DE-588)4130849-9 gnd rswk-swf Schur, Issai 1875-1941 (DE-588)118795627 p DE-604 Invariantentheorie (DE-588)4162209-1 s Quantenchaos (DE-588)4130849-9 s Pjateckij-Šapiro, Ilʹja I. 1929-2009 Sonstige (DE-588)122510887 oth Howe, Roger 1945- (DE-588)171158407 aut Perspectives on invariant theory Sarnak, Peter 1953- (DE-588)102958365X aut Arithmetic quantum chaos Israel Mathematical Conference: Israel Mathematical Conference proceedings 8 (DE-604)BV005098766 8 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007269663&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Howe, Roger 1945- Sarnak, Peter 1953- The Schur lectures (1992) Israel Mathematical Conference: Israel Mathematical Conference proceedings Schur, Issai 1875-1941 (DE-588)118795627 gnd Complex manifolds Hamiltonian systems Invariants Quantum chaos Invariantentheorie (DE-588)4162209-1 gnd Quantenchaos (DE-588)4130849-9 gnd |
| subject_GND | (DE-588)118795627 (DE-588)4162209-1 (DE-588)4130849-9 |
| title | The Schur lectures (1992) |
| title_alt | Perspectives on invariant theory Arithmetic quantum chaos |
| title_auth | The Schur lectures (1992) |
| title_exact_search | The Schur lectures (1992) |
| title_full | The Schur lectures (1992) Ilya Piatetski-Shapiro ... ed. |
| title_fullStr | The Schur lectures (1992) Ilya Piatetski-Shapiro ... ed. |
| title_full_unstemmed | The Schur lectures (1992) Ilya Piatetski-Shapiro ... ed. |
| title_short | The Schur lectures (1992) |
| title_sort | the schur lectures 1992 |
| topic | Schur, Issai 1875-1941 (DE-588)118795627 gnd Complex manifolds Hamiltonian systems Invariants Quantum chaos Invariantentheorie (DE-588)4162209-1 gnd Quantenchaos (DE-588)4130849-9 gnd |
| topic_facet | Schur, Issai 1875-1941 Complex manifolds Hamiltonian systems Invariants Quantum chaos Invariantentheorie Quantenchaos |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007269663&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005098766 |
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