Lie groups: structure, actions, and representations ; in honor of Joseph A. Wolf on the occasion of his 75th birthday
Saved in:
| Other Authors: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2013
|
| Series: | Progress in mathematics
306 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XIV, 413 S. Ill., graph. Darst. |
| ISBN: | 9781461471929 |
Staff View
MARC
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| 245 | 1 | 0 | |a Lie groups |b structure, actions, and representations ; in honor of Joseph A. Wolf on the occasion of his 75th birthday |c ed. by Alan Huckleberry ... |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2013 | |
| 300 | |a XIV, 413 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in mathematics |v 306 | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a K-theory | |
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| 650 | 4 | |a Differential equations, partial | |
| 650 | 4 | |a Mathematics | |
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Record in the Search Index
| _version_ | 1804150723276963840 |
|---|---|
| adam_text | Contents
Preface
............................................................................. ix
Real Group Orbits on Flag Manifolds
......................................... 1
Dmitri Akhiezer
1
Introduction
.................................................................. 1
2
Finiteness Theorem
.......................................................... 3
3
Embedding a Subgroup into a Parabolic One
.............................. 5
4
Factorizations of Reductive Groups
......................................... 6
5
Real Forms of Inner Type
................................................... 9
6
Matsuki Correspondence
.................................................... 14
7
Cycle Spaces
................................................................. 15
8
Complex Geometric Properties of the Crown
.............................. 17
9
The Schubert Domain
........................................................ 19
10
Complex Geometric Properties of Flag Domains
.......................... 21
References
......................................................................... 23
Complex Connections with Trivial Holonomy
................................ 25
Adrian Andrada, Maria Laura Barberis, and Isabel
Dotti
1
Introduction
.................................................................. 25
2
Preliminaries
................................................................. 27
3
Complex Connections with Trivial Holonomy
............................. 29
4
Complete Complex Connections with Parallel Torsion
and Trivial Holonomy
....................................................... 33
References
......................................................................... 38
Indefinite Harmonic Theory and Harmonic Spinors
........................ 41
Leticia
Barchini
and Roger Zierau
1
Introduction
.................................................................. 41
2
Comments on Indefinite Harmonic Theory
................................. 43
3
Harmonic Spinors
............................................................ 47
4
TheZ^Theory
............................................................... 49
References
......................................................................... 56
Xl
xii
Contents
Twistor Theory and the Harmonic Hull
....................................... 59
Michael Eastwood and Feng Xu
1
Introduction
.................................................................. 59
2
Harmonic Hull in Dimension
2.............................................. 62
3
Harmonic Hull in Dimension
4.............................................. 62
4
Generalities on Double Fibrations
.......................................... 70
5
Harmonic Hull in Higher Even Dimensions
................................ 73
6
Harmonic Hull in Odd Dimensions
......................................... 77
References
......................................................................... 79
Nilpotent Gelfand
Pairs and Spherical Transforms of Schwartz
Functions
П:
Taylor Expansions on Singular Sets
........................... 81
Véronique
Fischer,
Fulvio Ricci,
and Oksana Yakimova
1
Outline and Formulation of the Problem
................................... 82
2
Proof of Theorem
1.1
for TV Abelian
....................................... 87
Vі
3
TV Nonabelian: Structure of
^-Invariant
Polynomials on
ο φ
30
.......... 89
4
Fourier Analysis of AT-Equivariant Functions on
N ....................... 94
5
Proof of Proposition
4.3..................................................... 105
6
Conclusion
...................................................................
Ill
References
......................................................................... 112
Propagation of MuMplicity-Freeness Property for
Holomorphic Vector Bundles
................................................... 113
Toshiyuki Kobayashi
ł
Introduction
.................................................................. 114
2
Complex Geometry and Multiplicity-Free Theorem
....................... 115
3
Proof of Theorem
2.2........................................................ 118
4
Visible Actions on Complex Manifolds
.................................... 124
5
Multiplicity-Free Theorem for Associated Bundles
........................ 128
6
Proof of Proposition
5.2..................................................... 133
7
Concluding Remarks
......................................................... 135
References
......................................................................... 138
Poisson
Transforms for Line Bandies from the Shilov
Boundary to Bounded Symmetric Domains
................................... 141
Adam
Korányi
1
Introduction
.................................................................. 141
2
Genera]
Poisson
Transforms
................................................. 142
3
Preliminaries on Symmetric Domains
...................................... 144
4
Poisson
Transforms Between Line Bundles over
S
and
D
................ 150
5
Trivìalizatìons
and Explicit
Poisson
Kernels
............................... 151
6
The
Casimir
Operator
........................................................ 154
7
Remarks on Hua-Type Equations
........................................... 159
References
......................................................................... 162
Contents xiii
Center
(/(η),
Cascade of Orthogonal Roots, and a Construction
of Lipsman-Wolf
................................................................. 163
Bertram Kostant
1
Introduction
.................................................................. 164
2
Lipsman—Wolf Construction
................................................ 164
References
......................................................................... 173
Weak Harmonic
Maaß
Forms and the Principal Series for SL(2,
Ж)
...... 175
Peter
Kostelec,
Stephanie Treneer, and Dorothy Wallace
1
Introduction
.................................................................. 176
2
Preliminaries
................................................................. 176
3
Some Examples of Functions Constructed
from the Raising and Lowering Operators
.................................. 178
4
Constructing Weak Harmonic
Maaß
Forms from the Principal Series
__ 179
5
En, Fn andGn
................................................................ 181
6
Concluding Remarks
......................................................... 183
References
......................................................................... 184
Holomorphic Realization of Unitary Representations
of Banach-Lie Groups
........................................................... 185
Karl-Hermann Neeb
1
Introduction
.................................................................. 186
2
Holomorphic Banach Bundles
.............................................. 189
3
Hubert Spaces of Holomorphic Sections
................................... 195
4
Realizing Positive Energy Representations
................................. 207
A Equicontinuous Representations
............................................ 215
References
......................................................................... 221
The Segal-Bargmann Transform on Compact Symmetric
Spaces and Their Direct Limits
................................................. 225
Gestur
Ólafsson
and Keng Wiboonton
1
Introduction
.................................................................. 226
2
Basic Notations
.............................................................. 228
3
L2 Fourier Analysis
.......................................................... 229
4
The Fock Space?*, (Me)
.................................................... 234
5
Segal-Bargmann Transforms on L2(M) and L2(M)K
.................... 242
6
Propagations of Compact Symmetric Spaces
............................... 244
7
The Segal-Bargman Transform on the Direct Limit of
{L2(A/„)}„
....... 247
8
The Segal-Bargman Transform on the Direct Limit of {L2(Mn)Kn
}„__ 249
References
......................................................................... 251
Analysis on Flag Manifolds and Sobolev Inequalities
........................ 255
Bent 0rsted
1
Introduction
.................................................................. 255
2
Geometry of the Rank-1 Principal Series
................................... 256
3
Logarithmic Sobolev Inequalities for Rank-
1
Groups
..................... 261
xiv
Contents
4
Inequalities in the Noncompact Picture
..................................... 263
References
......................................................................... 270
Boundary Value Problems on Riemannian Symmetric Spaces
of the Noncompact Type
......................................................... 273
Toshio Oshima and Nobukazu Shimeno
1
Introduction
.................................................................. 273
2
Representations on Symmetric Spaces
...................................... 276
3
Construction of the
Hua Type
Operators
................................... 287
4
Examples
..................................................................... 294
References
......................................................................... 306
One-Step Spherical Functions of the Pair
(SU
(я
+1)
,
V
(η))
................ 309
Inés Pacharoni and Juan Tirao
1
Spherical Functions..........................................................
310
2
The Differential Operators
D
and
E........................................
314
3
Hypergeometrization
........................................................ 328
4
The Eigenvalues of
D
and
E
................................................ 333
5
The One-Step Spherical Functions
.......................................... 336
6
Matrix Orthogonal Polynomials
............................................. 345
References
......................................................................... 353
Chem—
Weil Theory for Certain Infinite-Dimensional Lie Groups
......... 355
Steven Rosenberg
1
Introduction
.................................................................. 355
2
General Comments on Chern—Weil Theory
................................ 358
3
Mapping Spaces and Their Characteristic Classes
......................... 361
4
Secondary Classes on
Ψ£
-Bundles
.......................................... 368
5
Characteristic Classes for Diffeomorphism Groups
........................ 371
6
Characteristic Classes and the Families Index Theorem
................... 373
References
......................................................................... 379
On the Structure of Finite Groups with Periodic Cohomology
............. 381
C.T.C. Wall
1
Introduction
.................................................................. 382
2
Notation and Preliminaries
.................................................. 384
3
Structure of ^ -Groups
...................................................... 387
4
Presentations of ^-Groups
.................................................. 389
5
Subgroups and Refinement of Type Classification
......................... 392
6
Free Orthogonal Actions
.................................................... 397
7
The Finiteness Obstruction
.................................................. 401
8
Application to the Space-Form Problem
.................................... 407
9
Space-Forms: Classification
................................................. 409
References
......................................................................... 411
Alan Huckleberry, Ivan Penkov, Gregg Zuckerman, Editors
Lie Groups: Structure, Actions, and Representations
In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday
Lie Groups: Structures, Actions, and Representations, In Honor of Joseph A. Wolf on
the Occasion of his 75th Birthday consists of invited expository and research articles
on new developments arising from Wolfs profound contributions to mathematics.
Due to Professor Wolf s broad interests, outstanding mathematicians and scholars in
a wide spectrum of mathematical fields contributed to the volume. Algebraic, geometric,
and analytic methods are employed. More precisely, finite groups and classical finite
dimensional, as well as infinite-dimensional Lie groups, and algebras play a role. Actions
on classical symmetric spaces, and on abstract homogeneous and representation spaces
are discussed. Contributions in the area of representation theory involve numerous
viewpoints, includingthat of algebraic groups and various analytic aspects of harmonic
analvsis.
Contributors:
D. Akhiezer
A. Andrada
M. L. Barberis
L. Barchini
I.
Dotti
M.
Eastwood
V. Fischer
T. Ko baya s h
і
A.
Korányi
B. Kostant
P.
Kostelec
K.-H.
Neeb
G. Olafsson
В.
Orsted
T. Oshima
I. Pacharoni
F. Ricci
S.
Rosenberg
N.
Shimeno
J.Tirao
S. Treneer
C.T.C. Wall
D.
Wallace
К.
Wiboonton
F. Xu
О.
Yakimova
R.
Zierau
birkhauser-science.com
|
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| genre_facet | Festschrift Konferenzschrift 2012 Bochum |
| id | DE-604.BV041261842 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:43:27Z |
| institution | BVB |
| isbn | 9781461471929 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026235646 |
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| physical | XIV, 413 S. Ill., graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Lie groups structure, actions, and representations ; in honor of Joseph A. Wolf on the occasion of his 75th birthday ed. by Alan Huckleberry ... Basel [u.a.] Birkhäuser 2013 XIV, 413 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 306 Mathematik K-theory Global analysis Differential equations, partial Mathematics Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf (DE-588)4016928-5 Festschrift gnd-content (DE-588)1071861417 Konferenzschrift 2012 Bochum gnd-content Lie-Gruppe (DE-588)4035695-4 s DE-604 Huckleberry, Alan 1941- (DE-588)108548996 edt Wolf, Joseph Albert 1936-2023 (DE-588)13068130X hnr Erscheint auch als Online-Ausgabe 978-1-4614-7193-6 Progress in mathematics 306 (DE-604)BV000004120 306 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026235646&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026235646&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Lie groups structure, actions, and representations ; in honor of Joseph A. Wolf on the occasion of his 75th birthday Progress in mathematics Mathematik K-theory Global analysis Differential equations, partial Mathematics Lie-Gruppe (DE-588)4035695-4 gnd |
| subject_GND | (DE-588)4035695-4 (DE-588)4016928-5 (DE-588)1071861417 |
| title | Lie groups structure, actions, and representations ; in honor of Joseph A. Wolf on the occasion of his 75th birthday |
| title_auth | Lie groups structure, actions, and representations ; in honor of Joseph A. Wolf on the occasion of his 75th birthday |
| title_exact_search | Lie groups structure, actions, and representations ; in honor of Joseph A. Wolf on the occasion of his 75th birthday |
| title_full | Lie groups structure, actions, and representations ; in honor of Joseph A. Wolf on the occasion of his 75th birthday ed. by Alan Huckleberry ... |
| title_fullStr | Lie groups structure, actions, and representations ; in honor of Joseph A. Wolf on the occasion of his 75th birthday ed. by Alan Huckleberry ... |
| title_full_unstemmed | Lie groups structure, actions, and representations ; in honor of Joseph A. Wolf on the occasion of his 75th birthday ed. by Alan Huckleberry ... |
| title_short | Lie groups |
| title_sort | lie groups structure actions and representations in honor of joseph a wolf on the occasion of his 75th birthday |
| title_sub | structure, actions, and representations ; in honor of Joseph A. Wolf on the occasion of his 75th birthday |
| topic | Mathematik K-theory Global analysis Differential equations, partial Mathematics Lie-Gruppe (DE-588)4035695-4 gnd |
| topic_facet | Mathematik K-theory Global analysis Differential equations, partial Mathematics Lie-Gruppe Festschrift Konferenzschrift 2012 Bochum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026235646&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026235646&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
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