Character Identities In The Twisted Endoscopy Of Real Reductive Groups

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Character Identities in the Twisted Endoscopy of Real Reductive Groups

Author : Paul Mezo
Publisher : American Mathematical Soc.
ISBN 13 : 0821875655
Total Pages : 106 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Character Identities in the Twisted Endoscopy of Real Reductive Groups by : Paul Mezo

Download or read book Character Identities in the Twisted Endoscopy of Real Reductive Groups written by Paul Mezo and published by American Mathematical Soc.. This book was released on 2013-02-26 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Representations of Reductive Groups

Author : Monica Nevins
Publisher : Birkhäuser
ISBN 13 : 3319234439
Total Pages : 545 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Representations of Reductive Groups by : Monica Nevins

Download or read book Representations of Reductive Groups written by Monica Nevins and published by Birkhäuser. This book was released on 2015-12-18 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last forty years, David Vogan has left an indelible imprint on the representation theory of reductive groups. His groundbreaking ideas have lead to deep advances in the theory of real and p-adic groups, and have forged lasting connections with other subjects, including number theory, automorphic forms, algebraic geometry, and combinatorics. Representations of Reductive Groups is an outgrowth of the conference of the same name, dedicated to David Vogan on his 60th birthday, which took place at MIT on May 19-23, 2014. This volume highlights the depth and breadth of Vogan's influence over the subjects mentioned above, and point to many exciting new directions that remain to be explored. Notably, the first article by McGovern and Trapa offers an overview of Vogan's body of work, placing his ideas in a historical context. Contributors: Pramod N. Achar, Jeffrey D. Adams, Dan Barbasch, Manjul Bhargava, Cédric Bonnafé, Dan Ciubotaru, Meinolf Geck, William Graham, Benedict H. Gross, Xuhua He, Jing-Song Huang, Toshiyuki Kobayashi, Bertram Kostant, Wenjing Li, George Lusztig, Eric Marberg, William M. McGovern, Wilfried Schmid, Kari Vilonen, Diana Shelstad, Peter E. Trapa, David A. Vogan, Jr., Nolan R. Wallach, Xiaoheng Wang, Geordie Williamson

Equivalent Definitions of Arthur Packets for Real Classical Groups

Author : J. Adams
Publisher : American Mathematical Society
ISBN 13 : 1470471051
Total Pages : 122 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Equivalent Definitions of Arthur Packets for Real Classical Groups by : J. Adams

Download or read book Equivalent Definitions of Arthur Packets for Real Classical Groups written by J. Adams and published by American Mathematical Society. This book was released on 2024-09-09 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Level One Algebraic Cusp Forms of Classical Groups of Small Rank

Author : Gaëtan Chenevier
Publisher : American Mathematical Soc.
ISBN 13 : 147041094X
Total Pages : 134 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Level One Algebraic Cusp Forms of Classical Groups of Small Rank by : Gaëtan Chenevier

Download or read book Level One Algebraic Cusp Forms of Classical Groups of Small Rank written by Gaëtan Chenevier and published by American Mathematical Soc.. This book was released on 2015-08-21 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Endoscopic Classification of Representations of Quasi-Split Unitary Groups

Author : Chung Pang Mok
Publisher : American Mathematical Soc.
ISBN 13 : 1470410419
Total Pages : 260 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Endoscopic Classification of Representations of Quasi-Split Unitary Groups by : Chung Pang Mok

Download or read book Endoscopic Classification of Representations of Quasi-Split Unitary Groups written by Chung Pang Mok and published by American Mathematical Soc.. This book was released on 2015-04-09 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Endoscopic Classification of Representations Orthogonal and Symplectic Groups

Author : James Arthur
Publisher : American Mathematical Soc.
ISBN 13 : 0821849905
Total Pages : 610 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Endoscopic Classification of Representations Orthogonal and Symplectic Groups by : James Arthur

Download or read book The Endoscopic Classification of Representations Orthogonal and Symplectic Groups written by James Arthur and published by American Mathematical Soc.. This book was released on 2013-10-31 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Automorphic Forms and Even Unimodular Lattices

Author : Gaëtan Chenevier
Publisher : Springer
ISBN 13 : 3319958917
Total Pages : 428 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Automorphic Forms and Even Unimodular Lattices by : Gaëtan Chenevier

Download or read book Automorphic Forms and Even Unimodular Lattices written by Gaëtan Chenevier and published by Springer. This book was released on 2019-02-28 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometric Aspects of the Trace Formula

Author : Werner Müller
Publisher : Springer
ISBN 13 : 3319948334
Total Pages : 461 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Geometric Aspects of the Trace Formula by : Werner Müller

Download or read book Geometric Aspects of the Trace Formula written by Werner Müller and published by Springer. This book was released on 2018-10-11 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Isolated Involutions in Finite Groups

Author : Rebecca Waldecker
Publisher : American Mathematical Soc.
ISBN 13 : 082188803X
Total Pages : 164 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Isolated Involutions in Finite Groups by : Rebecca Waldecker

Download or read book Isolated Involutions in Finite Groups written by Rebecca Waldecker and published by American Mathematical Soc.. This book was released on 2013-10-23 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a new proof of Glauberman's Z*-Theorem under the additional hypothesis that the simple groups involved in the centraliser of an isolated involution are known simple groups.

Non-cooperative Equilibria of Fermi Systems with Long Range Interactions

Author : Jean-Bernard Bru
Publisher : American Mathematical Soc.
ISBN 13 : 0821889761
Total Pages : 173 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Non-cooperative Equilibria of Fermi Systems with Long Range Interactions by : Jean-Bernard Bru

Download or read book Non-cooperative Equilibria of Fermi Systems with Long Range Interactions written by Jean-Bernard Bru and published by American Mathematical Soc.. This book was released on 2013-06-28 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors define a Banach space $\mathcal{M}_{1}$ of models for fermions or quantum spins in the lattice with long range interactions and make explicit the structure of (generalized) equilibrium states for any $\mathfrak{m}\in \mathcal{M}_{1}$. In particular, the authors give a first answer to an old open problem in mathematical physics--first addressed by Ginibre in 1968 within a different context--about the validity of the so-called Bogoliubov approximation on the level of states. Depending on the model $\mathfrak{m}\in \mathcal{M}_{1}$, the authors' method provides a systematic way to study all its correlation functions at equilibrium and can thus be used to analyze the physics of long range interactions. Furthermore, the authors show that the thermodynamics of long range models $\mathfrak{m}\in \mathcal{M}_{1}$ is governed by the non-cooperative equilibria of a zero-sum game, called here thermodynamic game.

On Some Aspects of Oscillation Theory and Geometry

Author : Bruno Bianchini
Publisher : American Mathematical Soc.
ISBN 13 : 0821887998
Total Pages : 208 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis On Some Aspects of Oscillation Theory and Geometry by : Bruno Bianchini

Download or read book On Some Aspects of Oscillation Theory and Geometry written by Bruno Bianchini and published by American Mathematical Soc.. This book was released on 2013-08-23 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this paper is to analyze some of the relationships between oscillation theory for linear ordinary differential equations on the real line (shortly, ODE) and the geometry of complete Riemannian manifolds. With this motivation the authors prove some new results in both directions, ranging from oscillation and nonoscillation conditions for ODE's that improve on classical criteria, to estimates in the spectral theory of some geometric differential operator on Riemannian manifolds with related topological and geometric applications. To keep their investigation basically self-contained, the authors also collect some, more or less known, material which often appears in the literature in various forms and for which they give, in some instances, new proofs according to their specific point of view.

The Sine-Gordon Equation in the Semiclassical Limit: Dynamics of Fluxon Condensates

Author : Robert J. Buckingham
Publisher : American Mathematical Soc.
ISBN 13 : 0821885456
Total Pages : 148 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Sine-Gordon Equation in the Semiclassical Limit: Dynamics of Fluxon Condensates by : Robert J. Buckingham

Download or read book The Sine-Gordon Equation in the Semiclassical Limit: Dynamics of Fluxon Condensates written by Robert J. Buckingham and published by American Mathematical Soc.. This book was released on 2013-08-23 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study the Cauchy problem for the sine-Gordon equation in the semiclassical limit with pure-impulse initial data of sufficient strength to generate both high-frequency rotational motion near the peak of the impulse profile and also high-frequency librational motion in the tails. They show that for small times independent of the semiclassical scaling parameter, both types of motion are accurately described by explicit formulae involving elliptic functions. These formulae demonstrate consistency with predictions of Whitham's formal modulation theory in both the hyperbolic (modulationally stable) and elliptic (modulationally unstable) cases.

On the Steady Motion of a Coupled System Solid-Liquid

Author : Josef Bemelmans
Publisher : American Mathematical Soc.
ISBN 13 : 0821887734
Total Pages : 102 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis On the Steady Motion of a Coupled System Solid-Liquid by : Josef Bemelmans

Download or read book On the Steady Motion of a Coupled System Solid-Liquid written by Josef Bemelmans and published by American Mathematical Soc.. This book was released on 2013-10-23 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the unconstrained (free) motion of an elastic solid B in a Navier-Stokes liquid L occupying the whole space outside B, under the assumption that a constant body force b is acting on B. More specifically, we are interested in the steady motion of the coupled system {B,L}, which means that there exists a frame with respect to which the relevant governing equations possess a time-independent solution. We prove the existence of such a frame, provided some smallness restrictions are imposed on the physical parameters, and the reference configuration of B satisfies suitable geometric properties.

Gromov, Cauchy and Causal Boundaries for Riemannian, Finslerian and Lorentzian Manifolds

Author : Jose Luis Flores
Publisher : American Mathematical Soc.
ISBN 13 : 0821887750
Total Pages : 88 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Gromov, Cauchy and Causal Boundaries for Riemannian, Finslerian and Lorentzian Manifolds by : Jose Luis Flores

Download or read book Gromov, Cauchy and Causal Boundaries for Riemannian, Finslerian and Lorentzian Manifolds written by Jose Luis Flores and published by American Mathematical Soc.. This book was released on 2013-10-23 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently, the old notion of causal boundary for a spacetime V has been redefined consistently. The computation of this boundary ∂V on any standard conformally stationary spacetime V=R×M, suggests a natural compactification MB associated to any Riemannian metric on M or, more generally, to any Finslerian one. The corresponding boundary ∂BM is constructed in terms of Busemann-type functions. Roughly, ∂BM represents the set of all the directions in M including both, asymptotic and "finite" (or "incomplete") directions. This Busemann boundary ∂BM is related to two classical boundaries: the Cauchy boundary ∂CM and the Gromov boundary ∂GM. The authors' aims are: (1) to study the subtleties of both, the Cauchy boundary for any generalized (possibly non-symmetric) distance and the Gromov compactification for any (possibly incomplete) Finsler manifold, (2) to introduce the new Busemann compactification MB, relating it with the previous two completions, and (3) to give a full description of the causal boundary ∂V of any standard conformally stationary spacetime. J. L. Flores and J. Herrera, University of Malaga, Spain, and M. Sánchez, University of Granada, Spain. Publisher's note.

Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms

Author : Andrew Knightly
Publisher : American Mathematical Soc.
ISBN 13 : 0821887440
Total Pages : 144 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms by : Andrew Knightly

Download or read book Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms written by Andrew Knightly and published by American Mathematical Soc.. This book was released on 2013-06-28 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors give an adelic treatment of the Kuznetsov trace formula as a relative trace formula on $\operatorname{GL}(2)$ over $\mathbf{Q}$. The result is a variant which incorporates a Hecke eigenvalue in addition to two Fourier coefficients on the spectral side. The authors include a proof of a Weil bound for the generalized twisted Kloosterman sums which arise on the geometric side. As an application, they show that the Hecke eigenvalues of Maass forms at a fixed prime, when weighted as in the Kuznetsov formula, become equidistributed relative to the Sato-Tate measure in the limit as the level goes to infinity.

On the Regularity of the Composition of Diffeomorphisms

Author : H. Inci
Publisher : American Mathematical Soc.
ISBN 13 : 0821887416
Total Pages : 72 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis On the Regularity of the Composition of Diffeomorphisms by : H. Inci

Download or read book On the Regularity of the Composition of Diffeomorphisms written by H. Inci and published by American Mathematical Soc.. This book was released on 2013-10-23 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: For M a closed manifold or the Euclidean space Rn we present a detailed proof of regularity properties of the composition of Hs-regular diffeomorphisms of M for s > 12dim⁡M+1.

On Central Critical Values of the Degree Four $L$-Functions for GSp(4): The Fundamental Lemma. III

Author : Masaaki Furusawa
Publisher : American Mathematical Soc.
ISBN 13 : 0821887424
Total Pages : 150 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis On Central Critical Values of the Degree Four $L$-Functions for GSp(4): The Fundamental Lemma. III by : Masaaki Furusawa

Download or read book On Central Critical Values of the Degree Four $L$-Functions for GSp(4): The Fundamental Lemma. III written by Masaaki Furusawa and published by American Mathematical Soc.. This book was released on 2013-08-23 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some time ago, the first and third authors proposed two relative trace formulas to prove generalizations of Böcherer's conjecture on the central critical values of the degree four -functions for , and proved the relevant fundamental lemmas. Recently, the first and second authors proposed an alternative third relative trace formula to approach the same problem and proved the relevant fundamental lemma. In this paper the authors extend the latter fundamental lemma and the first of the former fundamental lemmas to the full Hecke algebra. The fundamental lemma is an equality of two local relative orbital integrals. In order to show that they are equal, the authors compute them explicitly for certain bases of the Hecke algebra and deduce the matching.