Degenerate Principal Series For Symplectic And Odd Orthogonal Groups

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Degenerate Principal Series for Symplectic and Odd-Orthogonal Groups

Chris Jantzen
Degenerate Principal Series for Symplectic and Odd Orthogonal Groups Book PDF

Author : Chris Jantzen
Publisher : American Mathematical Soc.
Page : 114 pages
File Size : 50,9 Mb
Release : 1996-01-01
Category : Mathematics
ISBN : 9780821804827

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Degenerate Principal Series for Symplectic and Odd-Orthogonal Groups by Chris Jantzen Pdf

This memoir studies reducibility in a certain class of induced representations for and , where is -adic. In particular, it is concerned with representations obtained by inducing a one-dimensional representation from a maximal parabolic subgroup (i.e., degenerate principal series representations). Using the Jacquet module techniques of Tadić, the reducibility points for such representations are determined. When reducible, the composition series is described, giving Langlands data and Jacquet modules for the irreducible composition factors.

Degenerate Principal Series for Symplectic Groups

Chris Jantzen
Degenerate Principal Series for Symplectic Groups Book PDF

Author : Chris Jantzen
Publisher : American Mathematical Soc.
Page : 111 pages
File Size : 46,8 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825495

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Degenerate Principal Series for Symplectic Groups by Chris Jantzen Pdf

This paper is concerned with induced representations for $p$-adic groups. In particular, Jantzen examines the question of reducibility in the case where the inducing subgroup is a maximal parabolic subgroup of $Sp_{2n (F)$ and the inducing representation is one-dimensional. Two different approaches to this problem are used. The first, based on the work of Casselman and of Gustafson, reduces the problem to the corresponding question about an associated finite-dimensional representation of a certain Hecke algebra. The second approach is based on a technique of Tadi\'c and involves an analysis of Jacquet modules. This is used to obtain a more general result on induced representations, which may be used to deal with the problem when the inducing representation satisfies a regularity condition. The same basic argument is also applied in a case-by-case fashion to nonregular cases.

Automorphic Representations, L-functions and Applications

Stephen Rallis
Automorphic Representations L functions and Applications Book PDF

Author : Stephen Rallis
Publisher : Walter de Gruyter
Page : 442 pages
File Size : 40,8 Mb
Release : 2005
Category : Mathematics
ISBN : 3110179393

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Automorphic Representations, L-functions and Applications by Stephen Rallis Pdf

This volume is the proceedings of the conference on Automorphic Representations, L-functions and Applications: Progress and Prospects, held at the Department of Mathematics of The Ohio State University, March 27-30, 2003, in honor of the 60th birthday of Steve Rallis. The theory of automorphic representations, automorphic L-functions and their applications to arithmetic continues to be an area of vigorous and fruitful research. The contributed papers in this volume represent many of the most recent developments and directions, including Rankin-Selberg L-functions (Bump, Ginzburg-Jiang-Rallis, Lapid-Rallis) the relative trace formula (Jacquet, Mao-Rallis) automorphic representations (Gan-Gurevich, Ginzburg-Rallis-Soudry) representation theory of p-adic groups (Baruch, Kudla-Rallis, Moeglin, Cogdell-Piatetski-Shapiro-Shahidi) p-adic methods (Harris-Li-Skinner, Vigneras), and arithmetic applications (Chinta-Friedberg-Hoffstein). The survey articles by Bump, on the Rankin-Selberg method, and by Jacquet, on the relative trace formula, should be particularly useful as an introduction to the key ideas about these important topics. This volume should be of interest both to researchers and students in the area of automorphic representations, as well as to mathematicians in other areas interested in having an overview of current developments in this important field.

Geometry and Analysis of Automorphic Forms of Several Variables

Yoshinori Hamahata
Geometry and Analysis of Automorphic Forms of Several Variables Book PDF

Author : Yoshinori Hamahata
Publisher : World Scientific
Page : 388 pages
File Size : 55,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814355605

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Geometry and Analysis of Automorphic Forms of Several Variables by Yoshinori Hamahata Pdf

This volume contains contributions of principal speakers of the symposium on geometry and analysis of automorphic forms of several variables, held in September 2009 at Tokyo, Japan, in honor of Takayuki Oda''s 60th birthday. It presents both research and survey articles in the fields that are the main themes of his work. The volume may serve as a guide to developing areas as well as a resource for researchers who seek a broader view and for students who are beginning to explore automorphic form.

$L$ Functions for the Orthogonal Group

David Ginzburg,Ilya Piatetski-Shapiro,Ilʹi︠a︡ Iosifovich Pi︠a︡tet︠s︡kiĭ-Shapiro,Stephen Rallis
L Functions for the Orthogonal Group Book PDF

Author : David Ginzburg,Ilya Piatetski-Shapiro,Ilʹi︠a︡ Iosifovich Pi︠a︡tet︠s︡kiĭ-Shapiro,Stephen Rallis
Publisher : American Mathematical Soc.
Page : 233 pages
File Size : 47,9 Mb
Release : 1997
Category : Automorphic functions
ISBN : 9780821805435

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$L$ Functions for the Orthogonal Group by David Ginzburg,Ilya Piatetski-Shapiro,Ilʹi︠a︡ Iosifovich Pi︠a︡tet︠s︡kiĭ-Shapiro,Stephen Rallis Pdf

In this book, the authors establish global Rankin Selberg integrals which determine the standard [italic capital]L function for the group [italic capitals]GL[subscript italic]r x [italic capital]Gʹ, where [italic capital]Gʹ is an isometry group of a nondegenerate symmetric form. The class of automorphic representations considered here is for any pair [capital Greek]Pi1 [otimes/dyadic/Kronecker/tensor product symbol] [capital Greek]Pi2 where [capital Greek]Pi1 is generic cuspidal for [italic capitals]GL[subscript italic]r([italic capital]A) and [capital Greek]Pi2 is cuspidal for [italic capital]Gʹ([italic capital]A). The construction of these [italic capital]L functions involves the use of certain new "models" of local representations; these models generalize the usual generic models. The authors also computer local unramified factors in a new way using geometric ideas.

Automorphic Forms and Related Topics

Samuele Anni,Jay Jorgenson,Lejla Smajlović,Lynne Walling
Automorphic Forms and Related Topics Book PDF

Author : Samuele Anni,Jay Jorgenson,Lejla Smajlović,Lynne Walling
Publisher : American Mathematical Soc.
Page : 286 pages
File Size : 49,6 Mb
Release : 2019-06-19
Category : Automorphic forms
ISBN : 9781470435257

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Automorphic Forms and Related Topics by Samuele Anni,Jay Jorgenson,Lejla Smajlović,Lynne Walling Pdf

This volume contains the proceedings of the Building Bridges: 3rd EU/US Summer School and Workshop on Automorphic Forms and Related Topics, which was held in Sarajevo from July 11–22, 2016. The articles summarize material which was presented during the lectures and speed talks during the workshop. These articles address various aspects of the theory of automorphic forms and its relations with the theory of L-functions, the theory of elliptic curves, and representation theory. In addition to mathematical content, the workshop held a panel discussion on diversity and inclusion, which was chaired by a social scientist who has contributed to this volume as well. This volume is intended for researchers interested in expanding their own areas of focus, thus allowing them to “build bridges” to mathematical questions in other fields.

Bosonic Construction of Vertex Operator Para-Algebras from Symplectic Affine Kac-Moody Algebras

Michael David Weiner
Bosonic Construction of Vertex Operator Para Algebras from Symplectic Affine Kac Moody Algebras Book PDF

Author : Michael David Weiner
Publisher : American Mathematical Soc.
Page : 121 pages
File Size : 43,5 Mb
Release : 1998
Category : Kac-Moody algebras
ISBN : 9780821808665

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Bosonic Construction of Vertex Operator Para-Algebras from Symplectic Affine Kac-Moody Algebras by Michael David Weiner Pdf

Begins with the bosonic construction of four level -1/2 irreducible representations of the symplectic affine Kac-Moody Lie algebra Cl. The direct sum of two of these is given the structure of a vertex operator algebra (VOA), and the direct sum of the other two is given the structure of a twisted VOA-module. The dissertation includes the bosonic analog of the fermionic construction of a vertex operator superalgebra from the four level 1 irreducible modules of type Dl. No index. Annotation copyrighted by Book News, Inc., Portland, OR

The Degenerate Principal Series for Sp(2n)

Robert Gustafson
The Degenerate Principal Series for Sp 2n Book PDF

Author : Robert Gustafson
Publisher : American Mathematical Soc.
Page : 90 pages
File Size : 47,9 Mb
Release : 1981
Category : Lie groups
ISBN : 9780821822487

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The Degenerate Principal Series for Sp(2n) by Robert Gustafson Pdf

A series of induced representations of the symplectic group of 2[italic]n x 2[italic]n matrices over a [italic]p-adic field [italic]k is decomposed.

Generalized Symplectic Geometries and the Index of Families of Elliptic Problems

Liviu I. Nicolaescu
Generalized Symplectic Geometries and the Index of Families of Elliptic Problems Book PDF

Author : Liviu I. Nicolaescu
Publisher : American Mathematical Soc.
Page : 98 pages
File Size : 45,5 Mb
Release : 1997
Category : Geometry, Differential
ISBN : 9780821806210

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Generalized Symplectic Geometries and the Index of Families of Elliptic Problems by Liviu I. Nicolaescu Pdf

In this book, an index theorem is proved for arbitrary families of elliptic boundary value problems for Dirac operators and a surgery formula for the index of a family of Dirac operators on a closed manifold. Also obtained is a very general result on the cobordism invariance of the index of a family. All results are established by first symplectically rephrasing the problems and then using a generalized symplectic reduction technique. This provides a unified approach to all possible parameter spaces and all possible symmetries of a Dirac operator (eigh symmetries in the real case and two in the complex case). This text will also be of interest to those working in geometry and topology.

Wandering Vectors for Unitary Systems and Orthogonal Wavelets

Xingde Dai,David R. Larson
Wandering Vectors for Unitary Systems and Orthogonal Wavelets Book PDF

Author : Xingde Dai,David R. Larson
Publisher : American Mathematical Soc.
Page : 82 pages
File Size : 46,5 Mb
Release : 1998
Category : Functional analysis
ISBN : 9780821808009

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Wandering Vectors for Unitary Systems and Orthogonal Wavelets by Xingde Dai,David R. Larson Pdf

Investigates topological and structural properties of the set W(U) of all complete wandering vectors for a system U of unitary operators acting on a Hilbert space. The authors parameterize W(U) in terms of a fixed vector y and the set of all unitary operators which locally commute with U at y. No index. Annotation copyrighted by Book News, Inc., Portland, OR

Lie Groups and Subsemigroups with Surjective Exponential Function

Karl Heinrich Hofmann,Wolfgang Ruppert,Wolfgang A. F. Ruppert
Lie Groups and Subsemigroups with Surjective Exponential Function Book PDF

Author : Karl Heinrich Hofmann,Wolfgang Ruppert,Wolfgang A. F. Ruppert
Publisher : American Mathematical Soc.
Page : 189 pages
File Size : 46,7 Mb
Release : 1997
Category : Exponential functions
ISBN : 9780821806418

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Lie Groups and Subsemigroups with Surjective Exponential Function by Karl Heinrich Hofmann,Wolfgang Ruppert,Wolfgang A. F. Ruppert Pdf

In the structure theory of real Lie groups, there is still information lacking about the exponential function. Most notably, there are no general necessary and sufficient conditions for the exponential function to be surjective. It is surprising that for subsemigroups of Lie groups, the question of the surjectivity of the exponential function can be answered. Under nature reductions setting aside the "group part" of the problem, subsemigroups of Lie groups with surjective exponential function are completely classified and explicitly constructed in this memoir. There are fewer than one would think and the proofs are harder than one would expect, requiring some innovative twists. The main protagonists on the scene are SL(2, R) and its universal covering group, almost abelian solvable Lie groups (ie. vector groups extended by homotheties), and compact Lie groups. This text will also be of interest to those working in algebra and algebraic geometry.

The Finite Irreducible Linear 2-Groups of Degree 4

Dane Laurence Flannery
The Finite Irreducible Linear 2 Groups of Degree 4 Book PDF

Author : Dane Laurence Flannery
Publisher : American Mathematical Soc.
Page : 77 pages
File Size : 48,8 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821806258

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The Finite Irreducible Linear 2-Groups of Degree 4 by Dane Laurence Flannery Pdf

This memoir contains a complete classification of the finite irreducible 2-subgroups of $GL(4, {\mathbb C})$. Specifically, the author provides a parametrized list of representatives for the conjugacy classes of such groups, where each representative is defined by a generating set of monomial matrices. The problem is treated by a variety of techniques, including elementary character theory, a method for describing Hasse diagrams of submodule lattices, and calculation of 2-cohomology by means of the Lyndon-Hochschild-Serre spectral sequence. Related questions concerning isomorphism between the listed groups, and Schur indices of their defining characters, are also considered.It's features include: a complete classification of a class of $p$-groups; a first step towards extending presently available databases for use in proposed 'soluble quotient algorithms'; and, groups presented explicitly; may be used to test conjectures or to serve generally as a resource in group-theoretic computations.

Some Connections between Isoperimetric and Sobolev-type Inequalities

Serguei Germanovich Bobkov,Christian Houdré
Some Connections between Isoperimetric and Sobolev type Inequalities Book PDF

Author : Serguei Germanovich Bobkov,Christian Houdré
Publisher : American Mathematical Soc.
Page : 127 pages
File Size : 41,5 Mb
Release : 1997
Category : Gaussian processes
ISBN : 9780821806425

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Some Connections between Isoperimetric and Sobolev-type Inequalities by Serguei Germanovich Bobkov,Christian Houdré Pdf

For Borel probability measures on metric spaces, this text studies the interplay between isoperimetric and Sobolev-type inequalities. In particular the question of finding optimal constants via isoperimetric quantities is explored. Also given are necessary and sufficient conditions for the equivalence between the extremality of some sets in the isoperimetric problem and the validity of some analytic inequalities. The book devotes much attention to: the probability distributions on the real line; the normalized Lebesgue measure on the Euclidean sheres; and the canonical Gaussian measure on the Euclidean space.

The Structure of $k$-$CS$- Transitive Cycle-Free Partial Orders

Richard Warren
The Structure of k CS Transitive Cycle Free Partial Orders Book PDF

Author : Richard Warren
Publisher : American Mathematical Soc.
Page : 166 pages
File Size : 48,9 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821806227

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The Structure of $k$-$CS$- Transitive Cycle-Free Partial Orders by Richard Warren Pdf

The class of cycle-free partial orders (CFPOs) is defined, and the CFPOs fulfilling a natural transitivity assumption, called $k$-connected set transitivity ($k$-$CS$-transitivity), are analyzed in some detail. Classification in many of the interesting cases is given. This work generalizes Droste's classification of the countable $k$-transitive trees ($k \geq 2$). In a CFPO, the structure can branch downwards as well as upwards, and can do so repeatedly (though it never returns to the starting point by a cycle). Mostly it is assumed that $k \geq 3$ and that all maximal chains are finite. The main classification splits into the sporadic and skeletal cases. The former is complete in all cardinalities. The latter is performed only in the countable case. The classification is considerably more complicated than for trees, and skeletal CFPOs exhibit rich, elaborate and rather surprising behavior. Features: Lucid exposition of an important generalization of Droste's work Extended introduction clearly explaining the scope of the memoir Visually attractive topic with copious illustrations Self-contained material, requiring few prerequisites

Spectral Asymptotics on Degenerating Hyperbolic 3-Manifolds

Józef Dodziuk,Jay Jorgenson
Spectral Asymptotics on Degenerating Hyperbolic 3 Manifolds Book PDF

Author : Józef Dodziuk,Jay Jorgenson
Publisher : American Mathematical Soc.
Page : 90 pages
File Size : 49,7 Mb
Release : 1998
Category : Asymptotic expansions
ISBN : 9780821808375

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Spectral Asymptotics on Degenerating Hyperbolic 3-Manifolds by Józef Dodziuk,Jay Jorgenson Pdf

In this volume, the authors study asymptotics of the geometry and spectral theory of degenerating sequences of finite volume hyperbolic manifolds of three dimensions. Thurston's hyperbolic surgery theorem assets the existence of non-trivial sequences of finite volume hyperbolic three manifolds which converge to a three manifold with additional cusps. In the geometric aspect of their study, the authors use the convergence of hyperbolic metrics on the thick parts of the manifolds under consideration to investigate convergentce of tubes in the manifolds of the sequence to cusps of the limiting manifold. In the specral theory aspect of the work, they prove convergence of heat kernels. They then define a regualrized heat race associated to any finite volume, complete, hyperbolic three manifold, and study its asymptotic behaviour through degeneration. As an application of the analysis of the regularized heat trace, they study asymptotic behaviours of the spectral zeta function, determinant of the Laplacian, Selberg zeta function, and spectral counting functions through degeneration. The authors' methods are an adaptation to three dimensions of the earlier work of Jorgenson and Lundelius who investigated the asymptotic behaviour of spectral functions on degenerating families of finite area hyperbolic Riemann surfaces.