Matching Of Orbital Integrals On Gl 4 And Gsp 2

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Matching of Orbital Integrals on GL(4) and GSp(2)

Yuval Zvi Flicker
Matching of Orbital Integrals on GL 4 and GSp 2 Book PDF

Author : Yuval Zvi Flicker
Publisher : American Mathematical Soc.
Page : 112 pages
File Size : 48,9 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821809594

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Matching of Orbital Integrals on GL(4) and GSp(2) by Yuval Zvi Flicker Pdf

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 $H\backslash G/K$--where H is a subgroup containing the centralizer--plays a key role.

Matching of Orbital Integrals on Gl(4) and Gsp(2)

Yuval Zvi Flicker,Y Z Flicker
Matching of Orbital Integrals on Gl 4 and Gsp 2 Book PDF

Author : Yuval Zvi Flicker,Y Z Flicker
Publisher : Oxford University Press, USA
Page : 112 pages
File Size : 48,6 Mb
Release : 2014-09-11
Category : Orbit method
ISBN : 1470402440

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Matching of Orbital Integrals on Gl(4) and Gsp(2) by Yuval Zvi Flicker,Y Z Flicker Pdf

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

Rainer Weissauer
Endoscopy for GSp 4 and the Cohomology of Siegel Modular Threefolds Book PDF

Author : Rainer Weissauer
Publisher : Springer
Page : 384 pages
File Size : 43,7 Mb
Release : 2009-04-28
Category : Mathematics
ISBN : 9783540893066

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Endoscopy for GSp(4) and the Cohomology of Siegel Modular Threefolds by Rainer Weissauer Pdf

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 $GL(4)$

Solomon Friedberg,Hervé Jacquet
The Fundamental Lemma for the Shalika Subgroup of GL 4 Book PDF

Author : Solomon Friedberg,Hervé Jacquet
Publisher : American Mathematical Soc.
Page : 149 pages
File Size : 49,7 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821805404

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The Fundamental Lemma for the Shalika Subgroup of $GL(4)$ by Solomon Friedberg,Hervé Jacquet Pdf

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

Haruzo Hida,Dinakar Ramakrishnan,Freydoon Shahidi
Contributions to Automorphic Forms Geometry and Number Theory Book PDF

Author : Haruzo Hida,Dinakar Ramakrishnan,Freydoon Shahidi
Publisher : JHU Press
Page : 946 pages
File Size : 49,6 Mb
Release : 2004-03-11
Category : Mathematics
ISBN : 0801878608

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Contributions to Automorphic Forms, Geometry, and Number Theory by Haruzo Hida,Dinakar Ramakrishnan,Freydoon Shahidi Pdf

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)

Yuval Zvi Flicker
Automorphic Forms and Shimura Varieties of PGSp 2 Book PDF

Author : Yuval Zvi Flicker
Publisher : World Scientific
Page : 338 pages
File Size : 55,7 Mb
Release : 2005
Category : Mathematics
ISBN : 9789812564030

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Automorphic Forms and Shimura Varieties of PGSp (2) by Yuval Zvi Flicker Pdf

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

Doug Pickrell
Invariant Measures for Unitary Groups Associated to Kac Moody Lie Algebras Book PDF

Author : Doug Pickrell
Publisher : American Mathematical Soc.
Page : 125 pages
File Size : 46,6 Mb
Release : 2000
Category : Mathematics
ISBN : 9780821820681

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Invariant Measures for Unitary Groups Associated to Kac-Moody Lie Algebras by Doug Pickrell Pdf

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

Roger D. Nussbaum,Sjoerd M. Verduyn Lunel
Generalizations of the Perron Frobenius Theorem for Nonlinear Maps Book PDF

Author : Roger D. Nussbaum,Sjoerd M. Verduyn Lunel
Publisher : American Mathematical Soc.
Page : 113 pages
File Size : 53,6 Mb
Release : 1999
Category : Mappings
ISBN : 9780821809693

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Generalizations of the Perron-Frobenius Theorem for Nonlinear Maps by Roger D. Nussbaum,Sjoerd M. Verduyn Lunel Pdf

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

Sobolev Met Poincare

Piotr Hajłasz,Pekka Koskela
Sobolev Met Poincare Book PDF

Author : Piotr Hajłasz,Pekka Koskela
Publisher : American Mathematical Soc.
Page : 119 pages
File Size : 47,5 Mb
Release : 2000
Category : Inequalities
ISBN : 9780821820476

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Sobolev Met Poincare by Piotr Hajłasz,Pekka Koskela Pdf

There are several generalizations of the classical theory of Sobolev spaces as they are necessary for the applications to Carnot-Caratheodory spaces, subelliptic equations, quasiconformal mappings on Carnot groups and more general Loewner spaces, analysis on topological manifolds, potential theory on infinite graphs, analysis on fractals and the theory of Dirichlet forms. The aim of this paper is to present a unified approach to the theory of Sobolev spaces that covers applications to many of those areas. The variety of different areas of applications forces a very general setting. We are given a metric space $X$ equipped with a doubling measure $\mu$. A generalization of a Sobolev function and its gradient is a pair $u\in L^{1}_{\rm loc}(X)$, $0\leq g\in L^{p}(X)$ such that for every ball $B\subset X$ the Poincare-type inequality $ \intbar_{B} u-u_{B} \, d\mu \leq C r ( \intbar_{\sigma B} g^{p}\, d\mu)^{1/p}\,$ holds, where $r$ is the radius of $B$ and $\sigma\geq 1$, $C>0$ are fixed constants. Working in the above setting we show that basically all relevant results from the classical theory have their counterparts in our general setting. These include Sobolev-Poincare type embeddings, Rellich-Kondrachov compact embedding theorem, and even a version of the Sobolev embedding theorem on spheres. The second part of the paper is devoted to examples and applications in the above mentioned areas.

Study of the Critical Points at Infinity Arising from the Failure of the Palais-Smale Condition for n-Body Type Problems

Hasna Riahi
Study of the Critical Points at Infinity Arising from the Failure of the Palais Smale Condition for n Body Type Problems Book PDF

Author : Hasna Riahi
Publisher : American Mathematical Soc.
Page : 112 pages
File Size : 42,9 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821808733

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Study of the Critical Points at Infinity Arising from the Failure of the Palais-Smale Condition for n-Body Type Problems by Hasna Riahi Pdf

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 $q(t+T) = q(t),\; \forall t \in \mathfrak R$ (where $q_{i} \in \mathfrak R^{\ell}$, $\ell \ge 3$, $1 \le i \le n$, $q = (q_{1},...,q_{n})$ 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.

Inverse Invariant Theory and Steenrod Operations

Mara D. Neusel
Inverse Invariant Theory and Steenrod Operations Book PDF

Author : Mara D. Neusel
Publisher : American Mathematical Soc.
Page : 157 pages
File Size : 53,5 Mb
Release : 2000
Category : Mathematics
ISBN : 9780821820919

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Inverse Invariant Theory and Steenrod Operations by Mara D. Neusel Pdf

This book is intended for researchers and graduate students in commutative algebra, algebraic topology and invariant theory.

Control and Relaxation over the Circle

Bruce Hughes,Stratos Prassidis
Control and Relaxation over the Circle Book PDF

Author : Bruce Hughes,Stratos Prassidis
Publisher : American Mathematical Soc.
Page : 96 pages
File Size : 42,6 Mb
Release : 2000
Category : Mathematics
ISBN : 9780821820698

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Control and Relaxation over the Circle by Bruce Hughes,Stratos Prassidis Pdf

This work formulates and proves a geometric version of the fundamental theorem of algebraic K-theory which relates the K-theory of the Laurent polynomial extension of a ring to the K-theory of the ring. The geometric version relates the higher simple homotopy theory of the product of a finite complex and a circle with that of the complex. By using methods of controlled topology, we also obtain a geometric version of the fundamental theorem of lower algebraic K-theory. The main new innovation is a geometrically defined nil space.

Uniform Rectifiability and Quasiminimizing Sets of Arbitrary Codimension

Guy David,Stephen Semmes
Uniform Rectifiability and Quasiminimizing Sets of Arbitrary Codimension Book PDF

Author : Guy David,Stephen Semmes
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 43,9 Mb
Release : 2000
Category : Fourier analysis
ISBN : 9780821820483

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Uniform Rectifiability and Quasiminimizing Sets of Arbitrary Codimension by Guy David,Stephen Semmes Pdf

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

Algebraic and Strong Splittings of Extensions of Banach Algebras

William G. Bade,Harold G. Dales,Zinaida Alexandrovna Lykova
Algebraic and Strong Splittings of Extensions of Banach Algebras Book PDF

Author : William G. Bade,Harold G. Dales,Zinaida Alexandrovna Lykova
Publisher : American Mathematical Soc.
Page : 129 pages
File Size : 42,5 Mb
Release : 1999
Category : Banach algebras
ISBN : 9780821810583

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Algebraic and Strong Splittings of Extensions of Banach Algebras by William G. Bade,Harold G. Dales,Zinaida Alexandrovna Lykova Pdf

In this volume, the authors address the following: Let $A$ be a Banach algebra, and let $\sum\:\ 0\rightarrow I\rightarrow\frak A\overset\pi\to\longrightarrow A\rightarrow 0$ be an extension of $A$, where $\frak A$ is a Banach algebra and $I$ is a closed ideal in $\frak A$. The extension splits algebraically (respectively, splits strongly) if there is a homomorphism (respectively, continuous homomorphism) $\theta\: A\rightarrow\frak A$ such that $\pi\circ\theta$ is the identity on $A$. Consider first for which Banach algebras $A$ it is true that every extension of $A$ in a particular class of extensions splits, either algebraically or strongly, and second for which Banach algebras it is true that every extension of $A$ in a particular class which splits algebraically also splits strongly. These questions are closely related to the question when the algebra $\frak A$ has a (strong) Wedderburn decomposition. The main technique for resolving these questions involves the Banach cohomology group $\cal H2(A,E)$ for a Banach $A$-bimodule $E$, and related cohomology groups. Later chapters are particularly concerned with the case where the ideal $I$ is finite-dimensional. Results are obtained for many of the standard Banach algebras $A$.