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Lie Groups: Structure, Actions, and Representations: In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday 2013 ed. [Kietas viršelis]

Edited by Ivan Penkov, Edited by Gregg Zuckerman, Edited by Alan Huckleberry

Formatas: Hardback, 413 pages, aukštis x plotis: 235x155 mm, weight: 7627 g, XIV, 413 p., 1 Hardback
Serija: Progress in Mathematics 306
Išleidimo metai: 03-Aug-2013
Leidėjas: Birkhauser Boston Inc
ISBN-10: 1461471923
ISBN-13: 9781461471929

Kitos knygos pagal šią temą:

Algebra - (Šiuo metu turimos knygos: 3 prekės)
Groups & group theory
Functional analysis & transforms

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Formatas: Hardback, 413 pages, aukštis x plotis: 235x155 mm, weight: 7627 g, XIV, 413 p., 1 Hardback
Serija: Progress in Mathematics 306
Išleidimo metai: 03-Aug-2013
Leidėjas: Birkhauser Boston Inc
ISBN-10: 1461471923
ISBN-13: 9781461471929

Kitos knygos pagal šią temą:

Algebra - (Šiuo metu turimos knygos: 3 prekės)
Groups & group theory
Functional analysis & transforms

Pastovi nuoroda: https://www.kriso.lt/db/9781461471929.html

Raktažodžiai:

Lie groups

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 Wolf's profound contributions to mathematics. Due to Professor Wolfs 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, including that of algebraic groups and various analytic aspects of harmonic analysis.

Contributors

D. Akhiezer                         T. Oshima

A. Andrada                         I. Pacharoni

M. L. Barberis                    F. Ricci

L. Barchini                            S. Rosenberg

I. Dotti                                  N. Shimeno

M. Eastwood                     J.Tirao

V. Fischer                            S. Treneer

T. Kobayashi                       C.T.C. Wall

A. Korįnyi                           D. Wallace

B. Kostant                           K. Wiboonton

P. Kostelec                          F. Xu

K.-H. Neeb                          O. Yakimova

G. Olafsson                         R. Zierau

B. Ųrsted

Preface

Real Group Orbits on Flag Manifolds

(24)

Dmitri Akhiezer

1 Introduction

(2)

2 Finiteness Theorem

(2)

3 Embedding a Subgroup into a Parabolic One

(1)

4 Factorizations of Reductive Groups

(3)

5 Real Forms of Inner Type

(5)

6 Matsuki Correspondence

(1)

7 Cycle Spaces

(2)

8 Complex Geometric Properties of the Crown

(2)

9 The Schubert Domain

(2)

10 Complex Geometric Properties of Flag Domains

(4)

References

(2)

Complex Connections with Trivial Holonomy

(16)

Adrian Andrada

Maria Laura Barberis

Isabel Dotti

1 Introduction

(2)

2 Preliminaries

(2)

3 Complex Connections with Trivial Holonomy

(4)

4 Complete Complex Connections with Parallel Torsion and Trivial Holonomy

(8)

References

(3)

Indefinite Harmonic Theory and Harmonic Spinors

(18)

Leticia Barchini

Roger Zierau

1 Introduction

(2)

2 Comments on Indefinite Harmonic Theory

(4)

3 Harmonic Spinors

(2)

4 The L2-Theory

(10)

References

(3)

Twistor Theory and the Harmonic Hull

(22)

Michael Eastwood

Feng Xu

1 Introduction

(3)

2 Harmonic Hull in Dimension 2

(1)

3 Harmonic Hull in Dimension 4

(8)

4 Generalities on Double Fibrations

(3)

5 Harmonic Hull in Higher Even Dimensions

(4)

6 Harmonic Hull in Odd Dimensions

(4)

References

(2)

Nilpotent Gelfand Pairs and Spherical Transforms of Schwartz Functions II: Taylor Expansions on Singular Sets

(32)

Veronique Fischer

Fulvio Ricci

Oksana Yakimova

1 Outline and Formulation of the Problem

(5)

2 Proof of Theorem 1.1 for N Abelian

(2)

3 N Nonabelian: Structure of K-Invariant Polynomials

(5)

4 Fourier Analysis of K-Equivariant Functions on N

(11)

5 Proof of Proposition 4.3

105

(6)

6 Conclusion

111

(2)

References

112

(1)

Propagation of Multiplicity-Freeness Property for Holomorphic Vector Bundles

113

(28)

Toshiyuki Kobayashi

1 Introduction

114

(1)

2 Complex Geometry and Multiplicity-Free Theorem

115

(3)

3 Proof of Theorem 2.2

118

(6)

4 Visible Actions on Complex Manifolds

124

(4)

5 Multiplicity-Free Theorem for Associated Bundles

128

(5)

6 Proof of Proposition 5.2

133

(2)

7 Concluding Remarks

135

(6)

References

138

(3)

Poisson Transforms for Line Bundles from the Shilov Boundary to Bounded Symmetric Domains

141

(22)

Adam Koranyi

1 Introduction

141

(1)

2 General Poisson Transforms

142

(2)

3 Preliminaries on Symmetric Domains

144

(6)

4 Poisson Transforms Between Line Bundles over S and D

150

(1)

5 Trivializations and Explicit Poisson Kernels

151

(3)

6 The Casimir Operator

154

(5)

7 Remarks on Hua-Type Equations

159

(4)

References

162

(1)

Center U(n), Cascade of Orthogonal Roots, and a Construction of Lipsman-Wolf

163

(12)

Bertram Kostant

1 Introduction

164

(1)

2 Lipsman-Wolf Construction

164

(11)

References

173

(2)

Weak Harmonic Maaß Forms and the Principal Series for SL(2, R)

175

(10)

Peter Kostelec

Stephanie Treneer

Dorothy Wallace

1 Introduction

176

(1)

2 Preliminaries

176

(2)

3 Some Examples of Functions Constructed from the Raising and Lowering Operators

178

(1)

4 Constructing Weak Harmonic Maaβ Forms from the Principal Series

179

(2)

5 En, Fn and Gn

181

(2)

6 Concluding Remarks

183

(2)

References

184

(1)

Holomorphic Realization of Unitary Representations of Banach-Lie Groups

185

(40)

Karl-Hermann Neeb

1 Introduction

186

(3)

2 Holomorphic Banach Bundles

189

(6)

3 Hilbert Spaces of Holomorphic Sections

195

(12)

4 Realizing Positive Energy Representations

207

(18)

A Equicontinuous Representations

215

(6)

References

221

(4)

The Segal-Bargmann Transform on Compact Symmetric Spaces and Their Direct Limits

225

(30)

Gestur Olafsson

Keng Wiboonton

1 Introduction

226

(2)

2 Basic Notations

228

(1)

3 L2 Fourier Analysis

229

(5)

4 The Fock Space H1(MC)

234

(8)

5 Segal-Bargmann Transforms on L2(M) and L2(M)K

242

(2)

6 Propagations of Compact Symmetric Spaces

244

(3)

7 The Segal-Bargman Transform on the Direct Limit of {L2(Mn)}n

247

(2)

8 The Segal-Bargman Transform on the Direct Limit of {L2(Mn)Kn}n

249

(6)

References

251

(4)

Analysis on Flag Manifolds and Sobolev Inequalities

255

(18)

Bent Ørsted

1 Introduction

255

(1)

2 Geometry of the Rank-1 Principal Series

256

(5)

3 Logarithmic Sobolev Inequalities for Rank-1 Groups

261

(2)

4 Inequalities in the Noncompact Picture

263

(10)

References

270

(3)

Boundary Value Problems on Riemannian Symmetric Spaces of the Noncompact Type

273

(36)

Toshio Oshima

Nobukazu Shimeno

1 Introduction

273

(3)

2 Representations on Symmetric Spaces

276

(11)

3 Construction of the Hua Type Operators

287

(7)

4 Examples

294

(15)

References

306

(3)

One-Step Spherical Functions of the Pair (SU(n+1), U(n))

309

(46)

Ines Pacharoni

Juan Tirao

1 Spherical Functions

310

(4)

2 The Differential Operators D and E

314

(14)

3 Hypergeometrization

328

(5)

4 The Eigenvalues of D and E

333

(3)

5 The One-Step Spherical Functions

336

(9)

6 Matrix Orthogonal Polynomials

345

(10)

References

353

(2)

Chern-Weil Theory for Certain Infinite-Dimensional Lie Groups

355

(26)

Steven Rosenberg

1 Introduction

355

(3)

2 General Comments on Chern-Weil Theory

358

(3)

3 Mapping Spaces and Their Characteristic Classes

361

(7)

4 Secondary Classes on Ψ*0-Bundles

368

(3)

5 Characteristic Classes for Diffeomorphism Groups

371

(2)

6 Characteristic Classes and the Families Index Theorem

373

(8)

References

379

(2)

On the Structure of Finite Groups with Periodic Cohomology

381

C.T.C. Wall

1 Introduction

382

(2)

2 Notation and Preliminaries

384

(3)

3 Structure of P'-Groups

387

(2)

4 Presentations of P-Groups

389

(3)

5 Subgroups and Refinement of Type Classification

392

(5)

6 Free Orthogonal Actions

397

(4)

7 The Finiteness Obstruction

401

(6)

8 Application to the Space-Form Problem

407

(2)

9 Space-Forms: Classification

409

References

411

Lie Groups: Structure, Actions, and Representations: In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday 2013 ed. [Kietas viršelis]

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