Representations of Reductive p-adic Groups

Representations of Reductive p-adic Groups
Author: Anne-Marie Aubert
Publisher: Springer
Total Pages: 289
Release: 2019-04-16
Genre: Mathematics
ISBN: 9811366284

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This book consists of survey articles and original research papers in the representation theory of reductive p-adic groups. In particular, it includes a survey by Anne-Marie Aubert on the enormously influential local Langlands conjectures. The survey gives a precise and accessible formulation of many aspects of the conjectures, highlighting recent refinements, due to the author and her collaborators, and their current status. It also features an extensive account by Colin Bushnell of his work with Henniart on the fine structure of the local Langlands correspondence for general linear groups, beginning with a clear overview of Bushnell–Kutzko’s construction of cuspidal types for such groups. The remaining papers touch on a range of topics in this active area of modern mathematics: group actions on root data, explicit character formulas, classification of discrete series representations, unicity of types, local converse theorems, completions of Hecke algebras, p-adic symmetric spaces. All meet a high level of exposition. The book should be a valuable resource to graduate students and experienced researchers alike.

Representations of Real and P-adic Groups

Representations of Real and P-adic Groups
Author: Eng-chye Tan
Publisher: World Scientific
Total Pages: 426
Release: 2004
Genre: Mathematics
ISBN: 9812562508

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This invaluable volume collects the expanded lecture notes of thosetutorials. The topics covered include uncertainty principles forlocally compact abelian groups, fundamentals of representations of"p"-adic groups, the Harish?Chandra?Howe local characterexpansion, classification of the square-integrable representationsmodulo cuspidal data, Dirac cohomology and Vogan's conjecture, multiplicity-free actions and Schur?Weyl?Howe duality.

Representations of Reductive Groups

Representations of Reductive Groups
Author: Avraham Aizenbud
Publisher: American Mathematical Soc.
Total Pages: 450
Release: 2019-02-20
Genre: Representations of algebras
ISBN: 1470442841

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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.

Harmonic Analysis on Reductive, $p$-adic Groups

Harmonic Analysis on Reductive, $p$-adic Groups
Author: Robert S. Doran, Paul J. Sally, Jr., and Loren Spice
Publisher: American Mathematical Soc.
Total Pages: 294
Release: 2011
Genre: Harmonic analysis
ISBN: 0821874039

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Harmonic Analysis on Reductive Groups

Harmonic Analysis on Reductive Groups
Author: W. Barker
Publisher: Springer Science & Business Media
Total Pages: 395
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461204550

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A conference on Harmonic Analysis on Reductive Groups was held at Bowdoin College in Brunswick, Maine from July 31 to August 11, 1989. The stated goal of the conference was to explore recent advances in harmonic analysis on both real and p-adic groups. It was the first conference since the AMS Summer Sym posium on Harmonic Analysis on Homogeneous Spaces, held at Williamstown, Massachusetts in 1972, to cover local harmonic analysis on reductive groups in such detail and to such an extent. While the Williamstown conference was longer (three weeks) and somewhat broader (nilpotent groups, solvable groups, as well as semisimple and reductive groups), the structure and timeliness of the two meetings was remarkably similar. The program of the Bowdoin Conference consisted of two parts. First, there were six major lecture series, each consisting of several talks addressing those topics in harmonic analysis on real and p-adic groups which were the focus of intensive research during the previous decade. These lectures began at an introductory level and advanced to the current state of research. Sec ond, there was a series of single lectures in which the speakers presented an overview of their latest research.

Representations of Algebraic Groups

Representations of Algebraic Groups
Author: Jens Carsten Jantzen
Publisher: American Mathematical Soc.
Total Pages: 594
Release: 2003
Genre: Mathematics
ISBN: 082184377X

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Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.