Special Values Of Automorphic Cohomology Classes

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Special Values Of Automorphic Cohomology Classes

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Author : Mark Green
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-08-12

Special Values Of Automorphic Cohomology Classes written by Mark Green 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 2014-08-12 with Mathematics categories.

The authors study the complex geometry and coherent cohomology of nonclassical Mumford-Tate domains and their quotients by discrete groups. Their focus throughout is on the domains which occur as open -orbits in the flag varieties for and , regarded as classifying spaces for Hodge structures of weight three. In the context provided by these basic examples, the authors formulate and illustrate the general method by which correspondence spaces give rise to Penrose transforms between the cohomologies of distinct such orbits with coefficients in homogeneous line bundles.

Special Values Of Automorphic Cohomology Classes

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Author : Mark Green
language : en
Publisher:
Release Date : 2014

Special Values Of Automorphic Cohomology Classes written by Mark Green and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Automorphic forms categories.

"Volume 231, number 1088 (fifth of 5 numbers), September 2014."

Cohomology Of Arithmetic Groups And Automorphic Forms

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Author : Jean-Pierre Labesse
language : en
Publisher: Springer
Release Date : 2006-11-14

Cohomology Of Arithmetic Groups And Automorphic Forms written by Jean-Pierre Labesse and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Cohomology of arithmetic groups serves as a tool in studying possible relations between the theory of automorphic forms and the arithmetic of algebraic varieties resp. the geometry of locally symmetric spaces. These proceedings will serve as a guide to this still rapidly developing area of mathematics. Besides two survey articles, the contributions are original research papers.

Spectral Means Of Central Values Of Automorphic L Functions For Gl 2

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Author : Masao Tsuzuki
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-04-09

Spectral Means Of Central Values Of Automorphic L Functions For Gl 2 written by Masao Tsuzuki 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 2015-04-09 with Mathematics categories.

Starting with Green's functions on adele points of considered over a totally real number field, the author elaborates an explicit version of the relative trace formula, whose spectral side encodes the informaton on period integrals of cuspidal waveforms along a maximal split torus. As an application, he proves two kinds of asymptotic mean formula for certain central -values attached to cuspidal waveforms with square-free level.

Special Values Of Dirichlet Series Monodromy And The Periods Of Automorphic Forms

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Author : Peter Stiller
language : en
Publisher: American Mathematical Soc.
Release Date : 1984

Special Values Of Dirichlet Series Monodromy And The Periods Of Automorphic Forms written by Peter Stiller 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 1984 with Mathematics categories.

In this paper we explore a relationship that exists between the classical cusp form for subgroups of finite index in [italic]SL2([double-struck capital]Z) and certain differential equations, and we develop a connection between the equation's monodromy representation and the special values in the critical strip of the Dirichlet series associated to the cusp form.

Period Functions For Maass Wave Forms And Cohomology

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Author : R. Bruggeman
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-08-21

Period Functions For Maass Wave Forms And Cohomology written by R. Bruggeman 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 2015-08-21 with Mathematics categories.

The authors construct explicit isomorphisms between spaces of Maass wave forms and cohomology groups for discrete cofinite groups Γ⊂PSL2(R). In the case that Γ is the modular group PSL2(Z) this gives a cohomological framework for the results in Period functions for Maass wave forms. I, of J. Lewis and D. Zagier in Ann. Math. 153 (2001), 191-258, where a bijection was given between cuspidal Maass forms and period functions. The authors introduce the concepts of mixed parabolic cohomology group and semi-analytic vectors in principal series representation. This enables them to describe cohomology groups isomorphic to spaces of Maass cusp forms, spaces spanned by residues of Eisenstein series, and spaces of all Γ-invariant eigenfunctions of the Laplace operator. For spaces of Maass cusp forms the authors also describe isomorphisms to parabolic cohomology groups with smooth coefficients and standard cohomology groups with distribution coefficients. They use the latter correspondence to relate the Petersson scalar product to the cup product in cohomology.

Hodge Theory Complex Geometry And Representation Theory

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Author : Robert S. Doran
language : en
Publisher: American Mathematical Soc.
Release Date : 2014

Hodge Theory Complex Geometry And Representation Theory written by Robert S. Doran 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 2014 with Mathematics categories.

Contains carefully written expository and research articles. Expository papers include discussions of Noether-Lefschetz theory, algebraicity of Hodge loci, and the representation theory of SL2(R). Research articles concern the Hodge conjecture, Harish-Chandra modules, mirror symmetry, Hodge representations of Q-algebraic groups, and compactifications, distributions, and quotients of period domains.

Irreducible Almost Simple Subgroups Of Classical Algebraic Groups

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Author : Timothy C. Burness
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-06-26

Irreducible Almost Simple Subgroups Of Classical Algebraic Groups written by Timothy C. Burness 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 2015-06-26 with Mathematics categories.

Let be a simple classical algebraic group over an algebraically closed field of characteristic with natural module . Let be a closed subgroup of and let be a nontrivial -restricted irreducible tensor indecomposable rational -module such that the restriction of to is irreducible. In this paper the authors classify the triples of this form, where and is a disconnected almost simple positive-dimensional closed subgroup of acting irreducibly on . Moreover, by combining this result with earlier work, they complete the classification of the irreducible triples where is a simple algebraic group over , and is a maximal closed subgroup of positive dimension.

Imprimitive Irreducible Modules For Finite Quasisimple Groups

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Author : Gerhard Hiss
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-02-06

Imprimitive Irreducible Modules For Finite Quasisimple Groups written by Gerhard Hiss 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 2015-02-06 with Mathematics categories.

Motivated by the maximal subgroup problem of the finite classical groups the authors begin the classification of imprimitive irreducible modules of finite quasisimple groups over algebraically closed fields K. A module of a group G over K is imprimitive, if it is induced from a module of a proper subgroup of G. The authors obtain their strongest results when char(K)=0, although much of their analysis carries over into positive characteristic. If G is a finite quasisimple group of Lie type, they prove that an imprimitive irreducible KG-module is Harish-Chandra induced. This being true for \rm char(K) different from the defining characteristic of G, the authors specialize to the case char(K)=0 and apply Harish-Chandra philosophy to classify irreducible Harish-Chandra induced modules in terms of Harish-Chandra series, as well as in terms of Lusztig series. The authors determine the asymptotic proportion of the irreducible imprimitive KG-modules, when G runs through a series groups of fixed (twisted) Lie type. One of the surprising outcomes of their investigations is the fact that these proportions tend to 1, if the Lie rank of the groups tends to infinity. For exceptional groups G of Lie type of small rank, and for sporadic groups G, the authors determine all irreducible imprimitive KG-modules for arbitrary characteristic of K.

Hyperbolic Groupoids And Duality

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Author : Volodymyr Nekrashevych
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-08-21

Hyperbolic Groupoids And Duality written by Volodymyr Nekrashevych 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 2015-08-21 with Mathematics categories.

The author introduces a notion of hyperbolic groupoids, generalizing the notion of a Gromov hyperbolic group. Examples of hyperbolic groupoids include actions of Gromov hyperbolic groups on their boundaries, pseudogroups generated by expanding self-coverings, natural pseudogroups acting on leaves of stable (or unstable) foliation of an Anosov diffeomorphism, etc. The author describes a duality theory for hyperbolic groupoids. He shows that for every hyperbolic groupoid G there is a naturally defined dual groupoid G⊤ acting on the Gromov boundary of a Cayley graph of G. The groupoid G⊤ is also hyperbolic and such that (G⊤)⊤ is equivalent to G. Several classes of examples of hyperbolic groupoids and their applications are discussed.