Locally Analytic Vectors In Representations Of Locally Adic Analytic Groups

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Locally Analytic Vectors in Representations of Locally -adic Analytic Groups

Matthew J. Emerton
Locally Analytic Vectors in Representations of Locally adic Analytic Groups Book PDF

Author : Matthew J. Emerton
Publisher : American Mathematical Soc.
Page : 158 pages
File Size : 44,8 Mb
Release : 2017-07-13
Category : Geometry, Analytic
ISBN : 9780821875629

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Locally Analytic Vectors in Representations of Locally -adic Analytic Groups by Matthew J. Emerton Pdf

The goal of this memoir is to provide the foundations for the locally analytic representation theory that is required in three of the author's other papers on this topic. In the course of writing those papers the author found it useful to adopt a particular point of view on locally analytic representation theory: namely, regarding a locally analytic representation as being the inductive limit of its subspaces of analytic vectors (of various “radii of analyticity”). The author uses the analysis of these subspaces as one of the basic tools in his study of such representations. Thus in this memoir he presents a development of locally analytic representation theory built around this point of view. The author has made a deliberate effort to keep the exposition reasonably self-contained and hopes that this will be of some benefit to the reader.

p-adic Banach Space Representations

Dubravka Ban
p adic Banach Space Representations Book PDF

Author : Dubravka Ban
Publisher : Springer Nature
Page : 219 pages
File Size : 53,9 Mb
Release : 2023-02-11
Category : Mathematics
ISBN : 9783031226847

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p-adic Banach Space Representations by Dubravka Ban Pdf

This book systematically develops the theory of continuous representations on p-adic Banach spaces. Its purpose is to lay the foundations of the representation theory of reductive p-adic groups on p-adic Banach spaces, explain the duality theory of Schneider and Teitelbaum, and demonstrate its applications to continuous principal series. Written to be accessible to graduate students, the book gives a comprehensive introduction to the necessary tools, including Iwasawa algebras, p-adic measures and distributions, p-adic functional analysis, reductive groups, and smooth and algebraic representations. Part 1 culminates with the duality between Banach space representations and Iwasawa modules. This duality is applied in Part 2 for studying the intertwining operators and reducibility of the continuous principal series on p-adic Banach spaces. This monograph is intended to serve both as a reference book and as an introductory text for graduate students and researchers entering the area.

Automorphic Forms and Galois Representations

Fred Diamond,Payman L. Kassaei,Minhyong Kim
Automorphic Forms and Galois Representations Book PDF

Author : Fred Diamond,Payman L. Kassaei,Minhyong Kim
Publisher : Cambridge University Press
Page : 385 pages
File Size : 45,5 Mb
Release : 2014-10-16
Category : Mathematics
ISBN : 9781107691926

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Automorphic Forms and Galois Representations by Fred Diamond,Payman L. Kassaei,Minhyong Kim Pdf

Part one of a two-volume collection exploring recent developments in number theory related to automorphic forms and Galois representations.

Sur un Problème de Compatibilité Local-Global Localement Analytique

Christophe Breuil,Yiwen Ding
Sur un Probl me de Compatibilit Local Global Localement Analytique Book PDF

Author : Christophe Breuil,Yiwen Ding
Publisher : American Mathematical Society
Page : 166 pages
File Size : 41,7 Mb
Release : 2023-11-27
Category : Mathematics
ISBN : 9781470465476

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Sur un Problème de Compatibilité Local-Global Localement Analytique by Christophe Breuil,Yiwen Ding Pdf

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Geometry and Dynamics of Groups and Spaces

Mikhail Kapranov,Sergii Kolyada,Yu. I. Manin,Pieter Moree,Leonid Potyagailo
Geometry and Dynamics of Groups and Spaces Book PDF

Author : Mikhail Kapranov,Sergii Kolyada,Yu. I. Manin,Pieter Moree,Leonid Potyagailo
Publisher : Springer Science & Business Media
Page : 742 pages
File Size : 45,9 Mb
Release : 2008-03-05
Category : Mathematics
ISBN : 3764386088

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Geometry and Dynamics of Groups and Spaces by Mikhail Kapranov,Sergii Kolyada,Yu. I. Manin,Pieter Moree,Leonid Potyagailo Pdf

Alexander Reznikov (1960-2003) was a brilliant and highly original mathematician. This book presents 18 articles by prominent mathematicians and is dedicated to his memory. In addition it contains an influential, so far unpublished manuscript by Reznikov of book length. The book further provides an extensive survey on Kleinian groups in higher dimensions and some articles centering on Reznikov as a person.

Modern Trends in Algebra and Representation Theory

David Jordan,Nadia Mazza,Sibylle Schroll
Modern Trends in Algebra and Representation Theory Book PDF

Author : David Jordan,Nadia Mazza,Sibylle Schroll
Publisher : Cambridge University Press
Page : 407 pages
File Size : 45,9 Mb
Release : 2023-08-17
Category : Mathematics
ISBN : 9781009097352

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Modern Trends in Algebra and Representation Theory by David Jordan,Nadia Mazza,Sibylle Schroll Pdf

Expanding upon the material delivered during the LMS Autumn Algebra School 2020, this volume reflects the fruitful connections between different aspects of representation theory. Each survey article addresses a specific subject from a modern angle, beginning with an exploration of the representation theory of associative algebras, followed by the coverage of important developments in Lie theory in the past two decades, before the final sections introduce the reader to three strikingly different aspects of group theory. Written at a level suitable for graduate students and researchers in related fields, this book provides pure mathematicians with a springboard into the vast and growing literature in each area.

Rigid Character Groups, Lubin-Tate Theory, and (φ,Γ)-Modules

Laurent Berger,Peter Schneider,Bingyong Xie
Rigid Character Groups Lubin Tate Theory and Modules Book PDF

Author : Laurent Berger,Peter Schneider,Bingyong Xie
Publisher : American Mathematical Soc.
Page : 75 pages
File Size : 48,7 Mb
Release : 2020-04-03
Category : Education
ISBN : 9781470440732

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Rigid Character Groups, Lubin-Tate Theory, and (φ,Γ)-Modules by Laurent Berger,Peter Schneider,Bingyong Xie Pdf

The construction of the p-adic local Langlands correspondence for GL2(Qp) uses in an essential way Fontaine's theory of cyclotomic (φ,Γ)-modules. Here cyclotomic means that Γ=Gal(Qp(μp∞)/Qp) is the Galois group of the cyclotomic extension of Qp. In order to generalize the p-adic local Langlands correspondence to GL2(L), where L is a finite extension of Qp, it seems necessary to have at our disposal a theory of Lubin-Tate (φ,Γ)-modules. Such a generalization has been carried out, to some extent, by working over the p-adic open unit disk, endowed with the action of the endomorphisms of a Lubin-Tate group. The main idea of this article is to carry out a Lubin-Tate generalization of the theory of cyclotomic (φ,Γ)-modules in a different fashion. Instead of the p-adic open unit disk, the authors work over a character variety that parameterizes the locally L-analytic characters on oL. They study (φ,Γ)-modules in this setting and relate some of them to what was known previously.

On Operads, Bimodules and Analytic Functor

Nicola Gambino,André Joyal
On Operads Bimodules and Analytic Functor Book PDF

Author : Nicola Gambino,André Joyal
Publisher : American Mathematical Soc.
Page : 110 pages
File Size : 48,7 Mb
Release : 2017-09-25
Category : Algebra, Homological
ISBN : 9781470425760

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On Operads, Bimodules and Analytic Functor by Nicola Gambino,André Joyal Pdf

The authors develop further the theory of operads and analytic functors. In particular, they introduce the bicategory of operad bimodules, that has operads as -cells, operad bimodules as -cells and operad bimodule maps as 2-cells, and prove that it is cartesian closed. In order to obtain this result, the authors extend the theory of distributors and the formal theory of monads.

Cohomology of Arithmetic Groups

James W. Cogdell,Günter Harder,Stephen Kudla,Freydoon Shahidi
Cohomology of Arithmetic Groups Book PDF

Author : James W. Cogdell,Günter Harder,Stephen Kudla,Freydoon Shahidi
Publisher : Springer
Page : 304 pages
File Size : 53,8 Mb
Release : 2018-08-18
Category : Mathematics
ISBN : 9783319955490

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Cohomology of Arithmetic Groups by James W. Cogdell,Günter Harder,Stephen Kudla,Freydoon Shahidi Pdf

This book discusses the mathematical interests of Joachim Schwermer, who throughout his career has focused on the cohomology of arithmetic groups, automorphic forms and the geometry of arithmetic manifolds. To mark his 66th birthday, the editors brought together mathematical experts to offer an overview of the current state of research in these and related areas. The result is this book, with contributions ranging from topology to arithmetic. It probes the relation between cohomology of arithmetic groups and automorphic forms and their L-functions, and spans the range from classical Bianchi groups to the theory of Shimura varieties. It is a valuable reference for both experts in the fields and for graduate students and postdocs wanting to discover where the current frontiers lie.

Fundamental Solutions and Local Solvability for Nonsmooth Hörmander’s Operators

Marco Bramanti,Luca Brandolini,Maria Manfredini,Marco Pedroni
Fundamental Solutions and Local Solvability for Nonsmooth H rmander s Operators Book PDF

Author : Marco Bramanti,Luca Brandolini,Maria Manfredini,Marco Pedroni
Publisher : American Mathematical Soc.
Page : 79 pages
File Size : 45,6 Mb
Release : 2017-09-25
Category : Differential operators
ISBN : 9781470425593

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Fundamental Solutions and Local Solvability for Nonsmooth Hörmander’s Operators by Marco Bramanti,Luca Brandolini,Maria Manfredini,Marco Pedroni Pdf

The authors consider operators of the form in a bounded domain of where are nonsmooth Hörmander's vector fields of step such that the highest order commutators are only Hölder continuous. Applying Levi's parametrix method the authors construct a local fundamental solution for and provide growth estimates for and its first derivatives with respect to the vector fields. Requiring the existence of one more derivative of the coefficients the authors prove that also possesses second derivatives, and they deduce the local solvability of , constructing, by means of , a solution to with Hölder continuous . The authors also prove estimates on this solution.

Knot Invariants and Higher Representation Theory

Ben Webster
Knot Invariants and Higher Representation Theory Book PDF

Author : Ben Webster
Publisher : American Mathematical Soc.
Page : 141 pages
File Size : 44,9 Mb
Release : 2018-01-16
Category : Functor theory
ISBN : 9781470426507

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Knot Invariants and Higher Representation Theory by Ben Webster Pdf

The author constructs knot invariants categorifying the quantum knot variants for all representations of quantum groups. He shows that these invariants coincide with previous invariants defined by Khovanov for sl and sl and by Mazorchuk-Stroppel and Sussan for sl . The author's technique is to study 2-representations of 2-quantum groups (in the sense of Rouquier and Khovanov-Lauda) categorifying tensor products of irreducible representations. These are the representation categories of certain finite dimensional algebras with an explicit diagrammatic presentation, generalizing the cyclotomic quotient of the KLR algebra. When the Lie algebra under consideration is sl , the author shows that these categories agree with certain subcategories of parabolic category for gl .

Property ($T$) for Groups Graded by Root Systems

Mikhail Ershov,Andrei Jaikin-Zapirain,Martin Kassabov
Property T for Groups Graded by Root Systems Book PDF

Author : Mikhail Ershov,Andrei Jaikin-Zapirain,Martin Kassabov
Publisher : American Mathematical Soc.
Page : 135 pages
File Size : 41,5 Mb
Release : 2017-09-25
Category : Root systems (Algebra)
ISBN : 9781470426040

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Property ($T$) for Groups Graded by Root Systems by Mikhail Ershov,Andrei Jaikin-Zapirain,Martin Kassabov Pdf

The authors introduce and study the class of groups graded by root systems. They prove that if is an irreducible classical root system of rank and is a group graded by , then under certain natural conditions on the grading, the union of the root subgroups is a Kazhdan subset of . As the main application of this theorem the authors prove that for any reduced irreducible classical root system of rank and a finitely generated commutative ring with , the Steinberg group and the elementary Chevalley group have property . They also show that there exists a group with property which maps onto all finite simple groups of Lie type and rank , thereby providing a “unified” proof of expansion in these groups.

Hypercontractivity in Group von Neumann Algebras

Marius Junge,Carlos Palazuelos,Javier Parcet,Mathilde Perrin
Hypercontractivity in Group von Neumann Algebras Book PDF

Author : Marius Junge,Carlos Palazuelos,Javier Parcet,Mathilde Perrin
Publisher : American Mathematical Soc.
Page : 83 pages
File Size : 49,8 Mb
Release : 2017-09-25
Category : Group algebras
ISBN : 9781470425654

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Hypercontractivity in Group von Neumann Algebras by Marius Junge,Carlos Palazuelos,Javier Parcet,Mathilde Perrin Pdf

In this paper, the authors provide a combinatorial/numerical method to establish new hypercontractivity estimates in group von Neumann algebras. They illustrate their method with free groups, triangular groups and finite cyclic groups, for which they obtain optimal time hypercontractive inequalities with respect to the Markov process given by the word length and with an even integer. Interpolation and differentiation also yield general hypercontrativity for via logarithmic Sobolev inequalities. The authors' method admits further applications to other discrete groups without small loops as far as the numerical part—which varies from one group to another—is implemented and tested on a computer. The authors also develop another combinatorial method which does not rely on computational estimates and provides (non-optimal) hypercontractive inequalities for a larger class of groups/lengths, including any finitely generated group equipped with a conditionally negative word length, like infinite Coxeter groups. The authors' second method also yields hypercontractivity bounds for groups admitting a finite dimensional proper cocycle. Hypercontractivity fails for conditionally negative lengths in groups satisfying Kazhdan's property (T).

Systems of Transversal Sections Near Critical Energy Levels of Hamiltonian Systems in R

Naiara V. de Paulo,Pedro A. S. Salomão
Systems of Transversal Sections Near Critical Energy Levels of Hamiltonian Systems in R Book PDF

Author : Naiara V. de Paulo,Pedro A. S. Salomão
Publisher : American Mathematical Soc.
Page : 105 pages
File Size : 44,9 Mb
Release : 2018-03-19
Category : Hamiltonian systems
ISBN : 9781470428013

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Systems of Transversal Sections Near Critical Energy Levels of Hamiltonian Systems in R by Naiara V. de Paulo,Pedro A. S. Salomão Pdf

In this article the authors study Hamiltonian flows associated to smooth functions R R restricted to energy levels close to critical levels. They assume the existence of a saddle-center equilibrium point in the zero energy level . The Hamiltonian function near is assumed to satisfy Moser's normal form and is assumed to lie in a strictly convex singular subset of . Then for all small, the energy level contains a subset near , diffeomorphic to the closed -ball, which admits a system of transversal sections , called a foliation. is a singular foliation of and contains two periodic orbits and as binding orbits. is the Lyapunoff orbit lying in the center manifold of , has Conley-Zehnder index and spans two rigid planes in . has Conley-Zehnder index and spans a one parameter family of planes in . A rigid cylinder connecting to completes . All regular leaves are transverse to the Hamiltonian vector field. The existence of a homoclinic orbit to in follows from this foliation.

Boundary Conditions and Subelliptic Estimates for Geometric Kramers-Fokker-Planck Operators on Manifolds with Boundaries

Francis Nier
Boundary Conditions and Subelliptic Estimates for Geometric Kramers Fokker Planck Operators on Manifolds with Boundaries Book PDF

Author : Francis Nier
Publisher : American Mathematical Soc.
Page : 142 pages
File Size : 46,7 Mb
Release : 2018-03-19
Category : Electronic
ISBN : 9781470428020

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Boundary Conditions and Subelliptic Estimates for Geometric Kramers-Fokker-Planck Operators on Manifolds with Boundaries by Francis Nier Pdf

This article is concerned with the maximal accretive realizations of geometric Kramers-Fokker-Planck operators on manifolds with boundaries. A general class of boundary conditions is introduced which ensures the maximal accretivity and some global subelliptic estimates. Those estimates imply nice spectral properties as well as exponential decay properties for the associated semigroup. Admissible boundary conditions cover a wide range of applications for the usual scalar Kramer-Fokker-Planck equation or Bismut's hypoelliptic laplacian.