Matching Of Orbital Integrals On Gl 4 And Gsp 2

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Matching Of Orbital Integrals On Gl 4 And Gsp 2

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Author : Yuval Zvi Flicker
language : en
Publisher: American Mathematical Soc.
Release Date : 1999

Matching Of Orbital Integrals On Gl 4 And Gsp 2 written by Yuval Zvi Flicker and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.

The trace formula is the most powerful tool currently available to establish liftings of automorphic forms, as predicted by Langlands principle of functionality. The geometric part of the trace formula consists of orbital integrals, and the lifting is based on the fundamental lemma. The latter is an identity of the relevant orbital integrals for the unit elements of the Hecke algebras. This volume concerns a proof of the fundamental lemma in the classically most interesting case of Siegel modular forms, namely the symplectic group Sp(2). These orbital integrals are compared with those on GL(4), twisted by the transpose inverse involution. The technique of proof is elementary. Compact elements are decomposed into their absolutely semi-simple and topologically unipotent parts also in the twisted case; a double coset decomposition of the form H\ G/K--where H is a subgroup containing the centralizer--plays a key role.

Matching Of Orbital Integrals On Gl 4 And Gsp 2

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Author : Yuval Zvi Flicker
language : en
Publisher: Oxford University Press, USA
Release Date : 2014-09-11

Matching Of Orbital Integrals On Gl 4 And Gsp 2 written by Yuval Zvi Flicker and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with Orbit method categories.

The trace formula is the most powerful tool currently available to establish liftings of automorphic forms, as predicted by Langlands principle of functionality. The geometric part of the trace formula consists of orbital integrals, and the lifting is based on the fundamental lemma. The latter is an identity of the relevant orbital integrals for the unit elements of the Hecke algebras. This volume concerns a proof of the fundamental lemma in the classically most interesting case of Siegel modular forms, namely the symplectic group Sp(2). These orbital integrals are compared with those on GL(4), twisted by the transpose inverse involution. The technique of proof is elementary. Compact elements are decomposed into their absolutely semi-simple and topologically unipotent parts also in the twisted case; a double coset decomposition plays a key role.

Endoscopy For Gsp 4 And The Cohomology Of Siegel Modular Threefolds

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Author : Rainer Weissauer
language : en
Publisher: Springer
Release Date : 2009-04-28

Endoscopy For Gsp 4 And The Cohomology Of Siegel Modular Threefolds written by Rainer Weissauer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-28 with Mathematics categories.

This volume grew out of a series of preprints which were written and circulated - tween 1993 and 1994. Around the same time, related work was done independently by Harder [40] and Laumon [62]. In writing this text based on a revised version of these preprints that were widely distributed in summer 1995, I ?nally did not p- sue the original plan to completely reorganize the original preprints. After the long delay, one of the reasons was that an overview of the results is now available in [115]. Instead I tried to improve the presentation modestly, in particular by adding cross-references wherever I felt this was necessary. In addition, Chaps. 11 and 12 and Sects. 5. 1, 5. 4, and 5. 5 were added; these were written in 1998. I willgivea moredetailedoverviewofthecontentofthedifferentchaptersbelow. Before that I should mention that the two main results are the proof of Ramanujan’s conjecture for Siegel modular forms of genus 2 for forms which are not cuspidal representations associated with parabolic subgroups(CAP representations), and the study of the endoscopic lift for the group GSp(4). Both topics are formulated and proved in the ?rst ?ve chapters assuming the stabilization of the trace formula. All the remaining technical results, which are necessary to obtain the stabilized trace formula, are presented in the remaining chapters. Chapter 1 gathers results on the cohomology of Siegel modular threefolds that are used in later chapters, notably in Chap. 3. At the beginning of Chap.

The Fundamental Lemma For The Shalika Subgroup Of Gl 4

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Author : Solomon Friedberg
language : en
Publisher: American Mathematical Soc.
Release Date : 1996

The Fundamental Lemma For The Shalika Subgroup Of Gl 4 written by Solomon Friedberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.

The authors establish the fundamental lemma for a relative trace formula. The trace formula compares generic automorphic representations of [italic capitals]GS[italic]p(4) with automorphic representations of [italic capitals]GS(4) which are distinguished with respect to a character of the Shalika subgroup, the subgroup of matrices of 2 x 2 block form ([superscript italic]g [over] [subscript capital italic]X [and] 0 [over] [superscript italic]g). The fundamental lemma, giving the equality of the orbital integrals of the unit elements of the respective Hecke algebras, amounts to a comparison of certain exponential sums arising from these two different groups.

Contributions To Automorphic Forms Geometry And Number Theory

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Author : Haruzo Hida
language : en
Publisher: JHU Press
Release Date : 2004-03-11

Contributions To Automorphic Forms Geometry And Number Theory written by Haruzo Hida and has been published by JHU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-11 with Mathematics categories.

In Contributions to Automorphic Forms, Geometry, and Number Theory, Haruzo Hida, Dinakar Ramakrishnan, and Freydoon Shahidi bring together a distinguished group of experts to explore automorphic forms, principally via the associated L-functions, representation theory, and geometry. Because these themes are at the cutting edge of a central area of modern mathematics, and are related to the philosophical base of Wiles' proof of Fermat's last theorem, this book will be of interest to working mathematicians and students alike. Never previously published, the contributions to this volume expose the reader to a host of difficult and thought-provoking problems. Each of the extraordinary and noteworthy mathematicians in this volume makes a unique contribution to a field that is currently seeing explosive growth. New and powerful results are being proved, radically and continually changing the field's make up. Contributions to Automorphic Forms, Geometry, and Number Theory will likely lead to vital interaction among researchers and also help prepare students and other young mathematicians to enter this exciting area of pure mathematics. Contributors: Jeffrey Adams, Jeffrey D. Adler, James Arthur, Don Blasius, Siegfried Boecherer, Daniel Bump, William Casselmann, Laurent Clozel, James Cogdell, Laurence Corwin, Solomon Friedberg, Masaaki Furusawa, Benedict Gross, Thomas Hales, Joseph Harris, Michael Harris, Jeffrey Hoffstein, Hervé Jacquet, Dihua Jiang, Nicholas Katz, Henry Kim, Victor Kreiman, Stephen Kudla, Philip Kutzko, V. Lakshmibai, Robert Langlands, Erez Lapid, Ilya Piatetski-Shapiro, Dipendra Prasad, Stephen Rallis, Dinakar Ramakrishnan, Paul Sally, Freydoon Shahidi, Peter Sarnak, Rainer Schulze-Pillot, Joseph Shalika, David Soudry, Ramin Takloo-Bigash, Yuri Tschinkel, Emmanuel Ullmo, Marie-France Vignéras, Jean-Loup Waldspurger.

Automorphic Forms And Shimura Varieties Of Pgsp 2

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Author : Yuval Zvi Flicker
language : en
Publisher: World Scientific
Release Date : 2005

Automorphic Forms And Shimura Varieties Of Pgsp 2 written by Yuval Zvi Flicker and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

The area of automorphic representations is a natural continuation of studies in the 19th and 20th centuries on number theory and modular forms. A guiding principle is a reciprocity law relating infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called ?liftings.' This in-depth book concentrates on an initial example of the lifting, from a rank 2 symplectic group PGSp(2) to PGL(4), reflecting the natural embedding of Sp(2,ó) in SL(4, ó). It develops the technique of comparing twisted and stabilized trace formulae. It gives a detailed classification of the automorphic and admissible representation of the rank two symplectic PGSp(2) by means of a definition of packets and quasi-packets, using character relations and trace formulae identities. It also shows multiplicity one and rigidity theorems for the discrete spectrum.Applications include the study of the decomposition of the cohomology of an associated Shimura variety, thereby linking Galois representations to geometric automorphic representations.To put these results in a general context, the book concludes with a technical introduction to Langlands' program in the area of automorphic representations. It includes a proof of known cases of Artin's conjecture.

Invariant Measures For Unitary Groups Associated To Kac Moody Lie Algebras

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Author : Doug Pickrell
language : en
Publisher: American Mathematical Soc.
Release Date : 2000

Invariant Measures For Unitary Groups Associated To Kac Moody Lie Algebras written by Doug Pickrell and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

The main purpose of this paper is to prove the existence, and in some cases the uniqueness, of unitarily invariant measures on formal completions of groups associated to affine Kac-Moody algebras, and associated homogeneous spaces. The basic invariant measure is a natural generalization of Haar measure for a simply connected compact Lie group, and its projection to flag spaces is a generalization of the normalized invariant volume element. The other "invariant measures" are actually measures having values in line bundles over these spaces; these bundle-valued measures heuristically arise from coupling the basic invariant measure to Hermitian structures on associated line bundles, but in this infinite dimensional setting they are generally singular with respect to the basic invariant measure.

Generalizations Of The Perron Frobenius Theorem For Nonlinear Maps

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Author : Roger D. Nussbaum
language : en
Publisher: American Mathematical Soc.
Release Date : 1999

Generalizations Of The Perron Frobenius Theorem For Nonlinear Maps written by Roger D. Nussbaum and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.

The classical Frobenius-Perron Theorem establishes the existence of periodic points of certain linear maps in ${\mathbb R} DEGREESn$. The authors present generalizations of this theorem to nonlinea

Study Of The Critical Points At Infinity Arising From The Failure Of The Palais Smale Condition For N Body Type Problems

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Author : Hasna Riahi
language : en
Publisher: American Mathematical Soc.
Release Date : 1999

Study Of The Critical Points At Infinity Arising From The Failure Of The Palais Smale Condition For N Body Type Problems written by Hasna Riahi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.

In this work, the author examines the following: When the Hamiltonian system $m i \ddot{q} i + (\partial V/\partial q i) (t,q) =0$ with periodicity condition $q(t+T) = q(t),\; \forall t \in \germ R$ (where $q {i} \in \germ R{\ell}$, $\ell \ge 3$, $1 \le i \le n$, $q = (q {1},...,q {n})$ and $V = \sum V {ij}(t,q {i}-q {j})$ with $V {ij}(t,\xi)$ $T$-periodic in $t$ and singular in $\xi$ at $\xi = 0$) is posed as a variational problem, the corresponding functional does not satisfy the Palais-Smale condition and this leads to the notion of critical points at infinity. This volume is a study of these critical points at infinity and of the topology of their stable and unstable manifolds. The potential considered here satisfies the strong force hypothesis which eliminates collision orbits. The details are given for 4-body type problems then generalized to n-body type problems.

Uniform Rectifiability And Quasiminimizing Sets Of Arbitrary Codimension

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Author : Guy David
language : en
Publisher: American Mathematical Soc.
Release Date : 2000

Uniform Rectifiability And Quasiminimizing Sets Of Arbitrary Codimension written by Guy David and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

This book is intended for graduate students and research mathematicians interested in calculus of variations and optimal control; optimization.