Simple Supercuspidal L Packets Of Quasi Split Classical Groups
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Simple Supercuspidal L Packets Of Quasi Split Classical Groups
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Author : Masao Oi
language : en
Publisher: American Mathematical Society
Release Date : 2024-06-07
Simple Supercuspidal L Packets Of Quasi Split Classical Groups written by Masao Oi and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-07 with Mathematics categories.
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Representations Of Reductive P Adic Groups
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Author : Anne-Marie Aubert
language : en
Publisher: Springer
Release Date : 2019-04-16
Representations Of Reductive P Adic Groups written by Anne-Marie Aubert and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-16 with Mathematics categories.
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.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2007
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
On The Stabilization Of The Trace Formula
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Author : Laurent Clozel
language : en
Publisher: International Pressof Boston Incorporated
Release Date : 2011
On The Stabilization Of The Trace Formula written by Laurent Clozel and has been published by International Pressof Boston Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
Variations On A Theorem Of Tate
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Author : Stefan Patrikis
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-04-10
Variations On A Theorem Of Tate written by Stefan Patrikis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-10 with Algebraic number theory categories.
Let F be a number field. These notes explore Galois-theoretic, automorphic, and motivic analogues and refinements of Tate's basic result that continuous projective representations Gal(F¯¯¯¯/F)→PGLn(C) lift to GLn(C). The author takes special interest in the interaction of this result with algebraicity (for automorphic representations) and geometricity (in the sense of Fontaine-Mazur). On the motivic side, the author studies refinements and generalizations of the classical Kuga-Satake construction. Some auxiliary results touch on: possible infinity-types of algebraic automorphic representations; comparison of the automorphic and Galois “Tannakian formalisms” monodromy (independence-of-ℓ) questions for abstract Galois representations.
Endoscopic Classification Of Representations Of Quasi Split Unitary Groups
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Author : Chung Pang Mok
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-04-09
Endoscopic Classification Of Representations Of Quasi Split Unitary Groups written by Chung Pang Mok and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-09 with Mathematics categories.
In this paper the author establishes the endoscopic classification of tempered representations of quasi-split unitary groups over local fields, and the endoscopic classification of the discrete automorphic spectrum of quasi-split unitary groups over global number fields. The method is analogous to the work of Arthur on orthogonal and symplectic groups, based on the theory of endoscopy and the comparison of trace formulas on unitary groups and general linear groups.
The Local Langlands Conjecture For Gl 2
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Author : Colin J. Bushnell
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-29
The Local Langlands Conjecture For Gl 2 written by Colin J. Bushnell and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-29 with Mathematics categories.
The Local Langlands Conjecture for GL(2) contributes an unprecedented text to the so-called Langlands theory. It is an ambitious research program of already 40 years and gives a complete and self-contained proof of the Langlands conjecture in the case n=2. It is aimed at graduate students and at researchers in related fields. It presupposes no special knowledge beyond the beginnings of the representation theory of finite groups and the structure theory of local fields.
A Local Relative Trace Formula For The Ginzburg Rallis Model The Geometric Side
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Author : Chen Wan
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-12-02
A Local Relative Trace Formula For The Ginzburg Rallis Model The Geometric Side written by Chen Wan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-02 with Education categories.
Following the method developed by Waldspurger and Beuzart-Plessis in their proofs of the local Gan-Gross-Prasad conjecture, the author is able to prove the geometric side of a local relative trace formula for the Ginzburg-Rallis model. Then by applying such formula, the author proves a multiplicity formula of the Ginzburg-Rallis model for the supercuspidal representations. Using that multiplicity formula, the author proves the multiplicity one theorem for the Ginzburg-Rallis model over Vogan packets in the supercuspidal case.
Eisenstein Series And Automorphic L Functions
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Author : Freydoon Shahidi
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Eisenstein Series And Automorphic L Functions written by Freydoon Shahidi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
This book presents a treatment of the theory of $L$-functions developed by means of the theory of Eisenstein series and their Fourier coefficients, a theory which is usually referred to as the Langlands-Shahidi method. The information gathered from this method, when combined with the converse theorems of Cogdell and Piatetski-Shapiro, has been quite sufficient in establishing a number of new cases of Langlands functoriality conjecture; at present, some of these cases cannot be obtained by any other method. These results have led to far-reaching new estimates for Hecke eigenvalues of Maass forms, as well as definitive solutions to certain problems in analytic and algebraic number theory. This book gives a detailed treatment of important parts of this theory, including a rather complete proof of Casselman-Shalika's formula for unramified Whittaker functions as well as a general treatment of the theory of intertwining operators. It also covers in some detail the global aspects of the method as well as some of its applications to group representations and harmonic analysis. This book is addressed to graduate students and researchers who are interested in the Langlands program in automorphic forms and its connections with number theory.
The Endoscopic Classification Of Representations Orthogonal And Symplectic Groups
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Author : James Arthur
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-10-31
The Endoscopic Classification Of Representations Orthogonal And Symplectic Groups written by James Arthur and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-31 with Mathematics categories.
Within the Langlands program, endoscopy is a fundamental process for relating automorphic representations of one group with those of another. In this book, Arthur establishes an endoscopic classification of automorphic representations of orthogonal and symplectic groups . The representations are shown to occur in families (known as global -packets and -packets), which are parametrized by certain self-dual automorphic representations of an associated general linear group . The central result is a simple and explicit formula for the multiplicity in the automorphic discrete spectrum of for any representation in a family. The results of the volume have already had significant applications: to the local Langlands correspondence, the construction of unitary representations, the existence of Whittaker models, the analytic behaviour of Langlands -functions, the spectral theory of certain locally symmetric spaces, and to new phenomena for symplectic epsilon-factors. One can expect many more. In fact, it is likely that both the results and the techniques of the volume will have applications to almost all sides of the Langlands program. The methods are by comparison of the trace formula of with its stabilization (and a comparison of the twisted trace formula of with its stabilization, which is part of work in progress by Moeglin and Waldspurger). This approach is quite different from methods that are based on -functions, converse theorems, or the theta correspondence. The comparison of trace formulas in the volume ought to be applicable to a much larger class of groups. Any extension at all will have further important implications for the Langlands program.