Simple Supercuspidal $L$-Packets of Quasi-Split Classical Groups
Author: Masao Oi
Publisher: American Mathematical Society
Published: 2024-06-07
Total Pages: 174
ISBN-13: 1470469561
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Lanterna Rally
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Representations of Reductive p-adic Groups
Author: Anne-Marie Aubert
Publisher: Springer
Published: 2019-04-16
Total Pages: 289
ISBN-13: 9811366284
DOWNLOAD EBOOK →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
On the Stabilization of the Trace Formula
Author: Laurent Clozel
Publisher: International Pressof Boston Incorporated
Published: 2011
Total Pages: 527
ISBN-13: 9781571462275
DOWNLOAD EBOOK →Variations on a Theorem of Tate
Author: Stefan Patrikis
Publisher: American Mathematical Soc.
Published: 2019-04-10
Total Pages: 156
ISBN-13: 1470435403
DOWNLOAD EBOOK →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
Author: Chung Pang Mok
Publisher: American Mathematical Soc.
Published: 2015-04-09
Total Pages: 260
ISBN-13: 1470410419
DOWNLOAD EBOOK →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)
Author: Colin J. Bushnell
Publisher: Springer Science & Business Media
Published: 2006-08-29
Total Pages: 352
ISBN-13: 354031511X
DOWNLOAD EBOOK →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.
Regulators in Analysis, Geometry and Number Theory
Author: Alexander Reznikov
Publisher: Springer Science & Business Media
Published: 2000
Total Pages: 352
ISBN-13: 9780817641153
DOWNLOAD EBOOK →"This work is an outgrowth of a conference held at the Hebrew University in Jerusalem on Regulators in Analysis, Geometry and Number Theory, and should appeal to a broad audience of graduate students and research mathematicians."--BOOK JACKET.
A Local Relative Trace Formula for the Ginzburg-Rallis Model: The Geometric Side
Author: Chen Wan
Publisher: American Mathematical Soc.
Published: 2019-12-02
Total Pages: 90
ISBN-13: 1470436868
DOWNLOAD EBOOK →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
Author: Freydoon Shahidi
Publisher: American Mathematical Soc.
Published: 2010
Total Pages: 218
ISBN-13: 0821849891
DOWNLOAD EBOOK →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.
