Equivalent Definitions of Arthur Packets for Real Classical Groups
| Author | : J. Adams |
| Publisher | : American Mathematical Society |
| Total Pages | : 122 |
| Release | : 2024-09-09 |
| Genre | : Mathematics |
| ISBN | : 1470471051 |
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Equivalent Definitions Of Arthur Packets For Real Classical Groups
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On The Langlands Program: Endoscopy And Beyond
| Author | : Wee Teck Gan |
| Publisher | : World Scientific |
| Total Pages | : 449 |
| Release | : 2024-04-15 |
| Genre | : Mathematics |
| ISBN | : 9811285837 |
This is a collection of lecture notes from the minicourses in the December 2018 Langlands Workshop: Endoscopy and Beyond. The volume combines seven introductory chapters on trace formulas, local Arthur packets, and beyond endoscopy. It aims to introduce the endoscopy classification via a basic example of the trace formula for SL(2), explore the more refined questions on the structure of Arthur packets, and look beyond endoscopy following the suggestions of Langlands, Braverman-Kazhdan, Ngo, and Altuğ. The book is a helpful reference for undergraduates, postgraduates, and researchers.
Equivalent Definitions of Arthur Packets for Real Classical Groups
| Author | : Jeffrey Adams |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2024 |
| Genre | : Algebra |
| ISBN | : 9781470471057 |
Arthur has conjectured the existence of what are now known as Arthur packets of representations of reductive algebraic groups over local and global fields. In the case of special orthogonal and symplectic groups, he subsequently gave a definition of these packets, using local and global methods. For general real groups, an alternative approach to the definition of Arthur packets has been given by Adams-Barbasch-Vogan. This construction is purely local and uses geometric methods. Our main result is that these two definitions agree in the case of real special orthogonal and symplectic groups.
Simple Supercuspidal $L$-Packets of Quasi-Split Classical Groups
| Author | : Masao Oi |
| Publisher | : American Mathematical Society |
| Total Pages | : 174 |
| Release | : 2024-06-07 |
| Genre | : Mathematics |
| ISBN | : 1470469561 |
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Level One Algebraic Cusp Forms of Classical Groups of Small Rank
| Author | : Gaëtan Chenevier |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 134 |
| Release | : 2015-08-21 |
| Genre | : Mathematics |
| ISBN | : 147041094X |
The authors determine the number of level 1, polarized, algebraic regular, cuspidal automorphic representations of GLn over Q of any given infinitesimal character, for essentially all n≤8. For this, they compute the dimensions of spaces of level 1 automorphic forms for certain semisimple Z-forms of the compact groups SO7, SO8, SO9 (and G2) and determine Arthur's endoscopic partition of these spaces in all cases. They also give applications to the 121 even lattices of rank 25 and determinant 2 found by Borcherds, to level one self-dual automorphic representations of GLn with trivial infinitesimal character, and to vector valued Siegel modular forms of genus 3. A part of the authors' results are conditional to certain expected results in the theory of twisted endoscopy.
Representation Theory of Real Reductive Lie Groups
| Author | : James Arthur |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 258 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 0821843664 |
"The representation theory of real reductive groups is still incomplete, in spite of much progress made thus far. The papers in this volume were presented at The AMS-IMS-SIAM Joint Summer Research Conference "Representation Theory of Real Reductive Lie Groups" held in Snowbird, Utah in June 2006, with the aim of elucidating the problems that remain, as well as explaining what tools have recently become available to solve them. They represent a significant improvement in the exposition of some of the most important (and often least accessible) aspects of the literature." "This volume will be of interest to graduate students working in the harmonic analysis and representation theory of Lie groups. It will also appeal to experts working in closely related fields."--BOOK JACKET.
Eisenstein Series and Applications
| Author | : Wee Teck Gan |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 317 |
| Release | : 2007-12-22 |
| Genre | : Mathematics |
| ISBN | : 0817646396 |
Eisenstein series are an essential ingredient in the spectral theory of automorphic forms and an important tool in the theory of L-functions. They have also been exploited extensively by number theorists for many arithmetic purposes. Bringing together contributions from areas which do not usually interact with each other, this volume introduces diverse users of Eisenstein series to a variety of important applications. With this juxtaposition of perspectives, the reader obtains deeper insights into the arithmetic of Eisenstein series. The central theme of the exposition focuses on the common structural properties of Eisenstein series occurring in many related applications.
Representation Theory, Complex Analysis, and Integral Geometry
| Author | : Bernhard Krötz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 282 |
| Release | : 2011-12-13 |
| Genre | : Mathematics |
| ISBN | : 081764816X |
This volume targets graduate students and researchers in the fields of representation theory, automorphic forms, Hecke algebras, harmonic analysis, number theory.
The Langlands Classification and Irreducible Characters for Real Reductive Groups
| Author | : J. Adams |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 331 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 146120383X |
This monograph explores the geometry of the local Langlands conjecture. The conjecture predicts a parametrizations of the irreducible representations of a reductive algebraic group over a local field in terms of the complex dual group and the Weil-Deligne group. For p-adic fields, this conjecture has not been proved; but it has been refined to a detailed collection of (conjectural) relationships between p-adic representation theory and geometry on the space of p-adic representation theory and geometry on the space of p-adic Langlands parameters. This book provides and introduction to some modern geometric methods in representation theory. It is addressed to graduate students and research workers in representation theory and in automorphic forms.
