The Descent Map From Automorphic Representations Of Gl N To Classical Groups
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The Descent Map From Automorphic Representations Of Gl N To Classical Groups
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Author : David Soudry
language : en
Publisher: World Scientific
Release Date : 2011-06-30
The Descent Map From Automorphic Representations Of Gl N To Classical Groups written by David Soudry and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-30 with Mathematics categories.
This book introduces the method of automorphic descent, providing an explicit inverse map to the (weak) Langlands functorial lift from generic, cuspidal representations on classical groups to general linear groups. The essence of this method is the study of certain Fourier coefficients of Gelfand-Graev type, or of Fourier-Jacobi type when applied to certain residual Eisenstein series. This book contains a complete account of this automorphic descent, with complete, detailed proofs. The book will be of interest to graduate students and mathematicians, who specialize in automorphic forms and in representation theory of reductive groups over local fields. Relatively self-contained, the content of some of the chapters can serve as topics for graduate students seminars.
The Descent Map From Automorphic Representations Of Gl N To Classical Groups
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Author : David Ginzburg
language : en
Publisher: World Scientific
Release Date : 2011
The Descent Map From Automorphic Representations Of Gl N To Classical Groups written by David Ginzburg and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
1. Introduction. 1.1. Overview. 1.2. Formulas for the Weil representation. 1.3. The case, where H is unitary and the place v splits in E -- 2. On certain residual representations. 2.1. The groups. 2.2. The Eisenstein series to be considered. 2.3. L-groups and representations related to P[symbol]. 2.4. The residue representation. 2.5. The case of a maximal parabolic subgroup (r = 1). 2.6. A preliminary lemma on Eisenstein series on GL[symbol]. 2.7. Constant terms of E(h, f[symbol]). 2.8. Description of W(M[symbol], D[symbol]). 2.9. Continuation of the proff of Theorem 2.1 -- 3. Coefficients of Gelfand-Graev type, of Fourier-Jacobi type, and descent. 3.1. Gelfand-Graev coefficients. 3.2. Fourier-Jacobi coefficients. 3.3. Nilpotent orbits. 3.4. Global integrals representing L-functions I. 3.5. Global integrals representing L-functions II. 3.6. Definition of the descent. 3.7. Definition of Jacquet modules corresponding to Gelfand-Graev characters. 3.8. Definition of Jacquet modules corresponding to Fourier-Jacobi characters -- 4. Some double coset decompositions. 4.1. The space Q[symbol]. 4.2. A set of representatives for Q[symbol]. 4.3. Stabilizers. 4.4. The set Q\h[symbol] -- 5. Jacquet modules of parabolic inductions : Gelfand-Graev characters. 5.1. The case where K is a field. 5.2. The case K = k[symbol]k -- 6. Jacquet modules of parabolic inductions : Fourier-Jacobi characters. 6.1. The case where K is a field. 6.2. The case K = k[symbol]k -- 7. The tower property. 7.1. A general lemma on "exchanging roots". 7.2. A formula for constant terms of Gelfand-Graev coefficients. 7.3. Global Gelfand-Graev models for cuspidal representations. 7.4. The general case : H is neither split nor quasi-split. 7.5. Global Gelfand-Graev models for the residual representations E[symbol]. 7.6. A formula for constant terms of Fourier-Jacobi coefficients. 7.7. Global Fourier-Jacobi models for cuspidal representations. 7.8. Global Fourier-Jacobi models for the residual representations E[symbol]
Advances In The Theory Of Automorphic Forms And Their L Functions
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Author : Dihua Jiang
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-04-29
Advances In The Theory Of Automorphic Forms And Their L Functions written by Dihua Jiang 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 2016-04-29 with Mathematics categories.
This volume contains the proceedings of the workshop on “Advances in the Theory of Automorphic Forms and Their L-functions” held in honor of James Cogdell's 60th birthday, held from October 16–25, 2013, at the Erwin Schrödinger Institute (ESI) at the University of Vienna. The workshop and the papers contributed to this volume circle around such topics as the theory of automorphic forms and their L-functions, geometry and number theory, covering some of the recent approaches and advances to these subjects. Specifically, the papers cover aspects of representation theory of p-adic groups, classification of automorphic representations through their Fourier coefficients and their liftings, L-functions for classical groups, special values of L-functions, Howe duality, subconvexity for L-functions, Kloosterman integrals, arithmetic geometry and cohomology of arithmetic groups, and other important problems on L-functions, nodal sets and geometry.
Representation Theory Number Theory And Invariant Theory
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Author : Jim Cogdell
language : en
Publisher: Birkhäuser
Release Date : 2017-10-19
Representation Theory Number Theory And Invariant Theory written by Jim Cogdell and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-19 with Mathematics categories.
This book contains selected papers based on talks given at the "Representation Theory, Number Theory, and Invariant Theory" conference held at Yale University from June 1 to June 5, 2015. The meeting and this resulting volume are in honor of Professor Roger Howe, on the occasion of his 70th birthday, whose work and insights have been deeply influential in the development of these fields. The speakers who contributed to this work include Roger Howe's doctoral students, Roger Howe himself, and other world renowned mathematicians. Topics covered include automorphic forms, invariant theory, representation theory of reductive groups over local fields, and related subjects.
Geometric Aspects Of The Trace Formula
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Author : Werner Müller
language : en
Publisher: Springer
Release Date : 2018-10-11
Geometric Aspects Of The Trace Formula written by Werner Müller and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-11 with Mathematics categories.
The second of three volumes devoted to the study of the trace formula, these proceedings focus on automorphic representations of higher rank groups. Based on research presented at the 2016 Simons Symposium on Geometric Aspects of the Trace Formula that took place in Schloss Elmau, Germany, the volume contains both original research articles and articles that synthesize current knowledge and future directions in the field. The articles discuss topics such as the classification problem of representations of reductive groups, the structure of Langlands and Arthur packets, interactions with geometric representation theory, and conjectures on the global automorphic spectrum. Suitable for both graduate students and researchers, this volume presents the latest research in the field. Readers of the first volume Families of Automorphic Forms and the Trace Formula will find this a natural continuation of the study of the trace formula.
Automorphic Forms And Even Unimodular Lattices
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Author : Gaëtan Chenevier
language : en
Publisher: Springer
Release Date : 2019-02-28
Automorphic Forms And Even Unimodular Lattices written by Gaëtan Chenevier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-28 with Mathematics categories.
This book includes a self-contained approach of the general theory of quadratic forms and integral Euclidean lattices, as well as a presentation of the theory of automorphic forms and Langlands' conjectures, ranging from the first definitions to the recent and deep classification results due to James Arthur. Its connecting thread is a question about lattices of rank 24: the problem of p-neighborhoods between Niemeier lattices. This question, whose expression is quite elementary, is in fact very natural from the automorphic point of view, and turns out to be surprisingly intriguing. We explain how the new advances in the Langlands program mentioned above pave the way for a solution. This study proves to be very rich, leading us to classical themes such as theta series, Siegel modular forms, the triality principle, L-functions and congruences between Galois representations. This monograph is intended for any mathematician with an interest in Euclidean lattices, automorphic forms or number theory. A large part of it is meant to be accessible to non-specialists.
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.
Descent Construction For Gspin Groups
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Author : Joseph Hundley
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-09-06
Descent Construction For Gspin Groups written by Joseph Hundley 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 2016-09-06 with Mathematics categories.
In this paper the authors provide an extension of the theory of descent of Ginzburg-Rallis-Soudry to the context of essentially self-dual representations, that is, representations which are isomorphic to the twist of their own contragredient by some Hecke character. The authors' theory supplements the recent work of Asgari-Shahidi on the functorial lift from (split and quasisplit forms of) GSpin2n to GL2n.
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.