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| Author | : Chung Pang Mok |
| Publisher | : |
| Total Pages | : 248 |
| Release | : 2014 |
| Genre | : Algebraic number theory |
| ISBN | : 9781470422264 |
| Author | : Chung Pang Mok |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 260 |
| Release | : 2015-04-09 |
| Genre | : Mathematics |
| ISBN | : 1470410419 |
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.
| Author | : Werner Müller |
| Publisher | : Springer |
| Total Pages | : 581 |
| Release | : 2016-09-20 |
| Genre | : Mathematics |
| ISBN | : 3319414240 |
Featuring the work of twenty-three internationally-recognized experts, this volume explores the trace formula, spectra of locally symmetric spaces, p-adic families, and other recent techniques from harmonic analysis and representation theory. Each peer-reviewed submission in this volume, based on the Simons Foundation symposium on families of automorphic forms and the trace formula held in Puerto Rico in January-February 2014, is the product of intensive research collaboration by the participants over the course of the seven-day workshop. The goal of each session in the symposium was to bring together researchers with diverse specialties in order to identify key difficulties as well as fruitful approaches being explored in the field. The respective themes were counting cohomological forms, p-adic trace formulas, Hecke fields, slopes of modular forms, and orbital integrals.
| Author | : Anne-Marie Aubert |
| Publisher | : Springer |
| Total Pages | : 289 |
| Release | : 2019-04-16 |
| Genre | : Mathematics |
| ISBN | : 9811366284 |
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.
| Author | : James Arthur |
| Publisher | : |
| Total Pages | : |
| Release | : 2013 |
| Genre | : Algebraic number theory |
| ISBN | : 9781470409692 |
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 G. The representations are shown to occur in families (known as global L-packets and A-packets), which are parametrized by certain self-dual automorphic representations of an associated general linear group GL(N). The central result is a simple and explicit formula for the multiplicity in the automorphic discrete spectrum of G.
| 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.
| Author | : Toshiyuki Kobayashi |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 124 |
| Release | : 2015-10-27 |
| Genre | : Mathematics |
| ISBN | : 147041922X |
The authors give a complete classification of intertwining operators (symmetry breaking operators) between spherical principal series representations of and . They construct three meromorphic families of the symmetry breaking operators, and find their distribution kernels and their residues at all poles explicitly. Symmetry breaking operators at exceptional discrete parameters are thoroughly studied. The authors obtain closed formulae for the functional equations which the composition of the symmetry breaking operators with the Knapp-Stein intertwining operators of and satisfy, and use them to determine the symmetry breaking operators between irreducible composition factors of the spherical principal series representations of and . Some applications are included.
| Author | : Masao Oi |
| Publisher | : American Mathematical Society |
| Total Pages | : 174 |
| Release | : 2024-06-07 |
| Genre | : Mathematics |
| ISBN | : 1470469561 |
View the abstract.
| Author | : Farrell Brumley |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 394 |
| Release | : 2017 |
| Genre | : Mathematics |
| ISBN | : 147043573X |
Presents, through a mix of research and expository articles, some of the fascinating new directions in number theory and representation theory arising from recent developments in the Langlands program. Special emphasis is placed on nonclassical versions of the conjectural Langlands correspondences, where the underlying field is no longer the complex numbers.
| Author | : Michael Skeide |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 138 |
| Release | : 2016-03-10 |
| Genre | : Mathematics |
| ISBN | : 1470417383 |
In these notes the author presents a complete theory of classification of E0-semigroups by product systems of correspondences. As an application of his theory, he answers the fundamental question if a Markov semigroup admits a dilation by a cocycle perturbations of noise: It does if and only if it is spatial.
