Volume: 101; 2019; 450 pp; Hardcover
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Electronic ISBN: 978-1-4704-5157-8
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Representations of Reductive Groups
Share this pageEdited by Avraham Aizenbud; Dmitry Gourevitch; David Kazhdan; Erez M. Lapid
This volume contains the proceedings of the
Conference on Representation Theory and Algebraic Geometry, held in
honor of Joseph Bernstein, from June 11–16, 2017, at the Weizmann
Institute of Science and The Hebrew University of Jerusalem.
The topics reflect the decisive and diverse impact of Bernstein on
representation theory in its broadest scope. The themes include
representations of \(p\)-adic groups and Hecke algebras in all
characteristics, representations of real groups and supergroups, theta
correspondence, and automorphic forms.
Readership
Graduate students and researchers interested in representation theory and automorphic forms.
Table of Contents
Representations of Reductive Groups
Table of Contents pages: 1 2
- Cover Cover11
- Title page iii4
- Contents vii8
- Preface ix10
- Character values and Hochschild homology 112
- Schwartz space of parabolic basic affine space and asymptotic Hecke algebras 3142
- 1. Introduction and statement of the results 3142
- 2. Tempered representations and Harish-Chandra algebra 3445
- 3. Paley-Wiener theorems and the definition of the algebra \calJ(πΊ) 3647
- 4. Intertwining operators 3748
- 5. Intertwining operators in the cuspidal corank 1 case 3950
- 6. Proof of \reft{inter-schwartz} 4051
- 7. Some further questions 4152
- References 4253
- Explicit local Jacquet-Langlands correspondence: The non-dyadic wild case 4556
- On the Casselman-Jacquet functor 7384
- Introduction 7485
- 0.1. The Casselman-Jacquet functor 7485
- 0.2. Functorial interpretation of the Casselman-Jacquet functor 7586
- 0.3. The pseudo-identity functor and the ULA condition 7788
- 0.4. The β2nd adjointnessβ conjecture 7889
- 0.5. Organization of the paper 7990
- 0.6. Conventions and notation 8091
- 0.7. How to get rid of DG categories? 8091
- 0.8. Acknowledgements 8192
- 1. Recollections 8192
- 2. Casselman-Jacquet functor as averaging 91102
- 3. The pseudo-identity functor 99110
- 4. The case of a symmetric pair 107118
- References 112123
- Periods and theta correspondence 113124
- Generalized and degenerate Whittaker quotients and Fourier coefficients 133144
- Geometric approach to the fermionic Fock space, via flag varieties and representations of algebraic (super)groups 155166
- Representations of a π-adic group in characteristic π 171182
- I. Introduction 172183
- II. Some general algebra 178189
- III. Classification theorem for πΊ 186197
- III.1. Admissibility, πΎ-invariants, and scalar extension 186197
- III.2. Decomposition Theorem for πΊ 187198
- III.3. The representations πΌ_{πΊ}(π,π,π) 190201
- III.4. Supersingular representations 193204
- III.5. Classification of irreducible admissible π -representations of πΊ 195206
- IV. Classification theorem for π»(πΊ) 196207
- IV.1. Pro-π Iwahori Hecke ring 196207
- IV.2. Parabolic induction \Ind_{π}^{π»(πΊ)} 197208
- IV.3. The π»(πΊ)_{π }-module \St_{π}^{π»(πΊ)}(\cV) 198209
- IV.4. The module πΌ_{π»(πΊ)}(π,\cV,π) 200211
- IV.5. Classification of simple modules over the pro-π Iwahori Hecke algebra 202213
- V. Applications 203214
- VI. Appendix: Eight inductions \Mod_{π }(π»(π))β\Mod_{π }(π»(πΊ)) 206217
- References 208219
- On the support of matrix coefficients of supercuspidal representations of the general linear group over a local non-archimedean field 211222
- On the generalized Springer correspondence 219230
- The modular pro-π Iwahori-Hecke πΈπ₯π‘-algebra 255266
- 1. Introduction 256267
- 2. Notations and preliminaries 257268
- 3. The \Ext-algebra 271282
- 4. Representing cohomological operations on resolutions 273284
- 5. The product in πΈ* 278289
- 6. An involutive anti-automorphism of the algebra πΈ* 287298
- 7. Dualities 290301
- 8. The structure of πΈ^{π} 302313
- References 306317
- Affine Hecke algebras and the conjectures of Hiraga, Ichino and Ikeda on the Plancherel density 309320
- 1. Introduction 310321
- 2. The conjecture of Hiraga, Ichino and Ikeda 312323
- 2.1. The decomposition of the trace 313324
- 2.2. Normalization of Haar measure 314325
- 2.3. Local Langlands parameters 314325
- 2.4. πΏ-functions and π factors 316327
- 2.5. A conjectural tempered local Langlands correspondence 317328
- 2.6. The conjectures of Hiraga, Ichino and Ikeda 318329
- 2.7. Known results and further comments 319330
- 3. The Plancherel formula for affine Hecke algebras 319330
- 3.1. The Bernstein center 320331
- 3.2. Types, Hecke algebras and Plancherel measure 320331
- 3.3. Affine Hecke algebras as Hilbert algebras 322333
- 3.4. A formula for the trace of an affine Hecke algebra 323334
- 3.5. Spectral decomposition of π 324335
- 3.6. Residual cosets and their properties 326337
- 3.7. Deformation of discrete series and the computation of π_{\Hc,πΏ} 327338
- 3.8. Central characters and Langlands parameters 328339
- 4. Lusztigβs representations of unipotent reduction and spectral transfer maps. Main result. 329340
- References 346357
Table of Contents pages: 1 2