The Endoscopic Classification of Representations Orthogonal and Symplectic Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Endoscopic Classification of Representations Orthogonal and Symplectic Groups write by James Arthur. This book was released on 2013-10-31. The Endoscopic Classification of Representations Orthogonal and Symplectic Groups available in PDF, EPUB and Kindle. 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.
Endoscopic Classification of Representations of Quasi-Split Unitary Groups
Endoscopic Classification of Representations of Quasi-Split Unitary Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Endoscopic Classification of Representations of Quasi-Split Unitary Groups write by Chung Pang Mok. This book was released on 2015-04-09. Endoscopic Classification of Representations of Quasi-Split Unitary Groups available in PDF, EPUB and Kindle. 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.
Character Identities in the Twisted Endoscopy of Real Reductive Groups
Character Identities in the Twisted Endoscopy of Real Reductive Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Character Identities in the Twisted Endoscopy of Real Reductive Groups write by Paul Mezo. This book was released on 2013-02-26. Character Identities in the Twisted Endoscopy of Real Reductive Groups available in PDF, EPUB and Kindle. Suppose $G$ is a real reductive algebraic group, $\theta$ is an automorphism of $G$, and $\omega$ is a quasicharacter of the group of real points $G(\mathbf{R})$. Under some additional assumptions, the theory of twisted endoscopy associates to this triple real reductive groups $H$. The Local Langlands Correspondence partitions the admissible representations of $H(\mathbf{R})$ and $G(\mathbf{R})$ into $L$-packets. The author proves twisted character identities between $L$-packets of $H(\mathbf{R})$ and $G(\mathbf{R})$ comprised of essential discrete series or limits of discrete series.
Families of Automorphic Forms and the Trace Formula
Families of Automorphic Forms and the Trace Formula - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Families of Automorphic Forms and the Trace Formula write by Werner Müller. This book was released on 2016-09-20. Families of Automorphic Forms and the Trace Formula available in PDF, EPUB and Kindle. 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.
On The Langlands Program: Endoscopy And Beyond
On The Langlands Program: Endoscopy And Beyond - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On The Langlands Program: Endoscopy And Beyond write by Wee Teck Gan. This book was released on 2024-04-15. On The Langlands Program: Endoscopy And Beyond available in PDF, EPUB and Kindle. 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.
