Representations of Real and P adic Groups

As part of the program, tutorials for graduate students and junior researchers were given by leading experts in the field.This invaluable volume collects the expanded lecture notes of those tutorials.

Author: Eng-chye Tan

Publisher: World Scientific

ISBN: 981238779X

Category: Science

Page: 415

View: 698

The Institute for Mathematical Sciences at the National University of Singapore hosted a research program on ?Representation Theory of Lie Groups? from July 2002 to January 2003. As part of the program, tutorials for graduate students and junior researchers were given by leading experts in the field.This invaluable volume collects the expanded lecture notes of those tutorials. The topics covered include uncertainty principles for locally compact abelian groups, fundamentals of representations of p-adic groups, the Harish-Chandra-Howe local character expansion, classification of the square-integrable representations modulo cuspidal data, Dirac cohomology and Vogan's conjecture, multiplicity-free actions and Schur-Weyl-Howe duality.The lecturers include Tomasz Przebinda from the University of Oklahoma, USA; Gordan Savin from the University of Utah, USA; Stephen DeBacker from Harvard University, USA; Marko Tadi? from the University of Zagreb, Croatia; Jing-Song Huang from The Hong Kong University of Science and Technology, Hong Kong; Pavle Pand?i? from the University of Zagreb, Croatia; Chal Benson and Gail Ratcliff from East Carolina University, USA; and Roe Goodman from Rutgers University, USA.

Geometry and Representation Theory of Real and p adic groups

Here is a rough outline of the mathematical content. (The editors beg the indulgence of the readers for any lapses in this preface in the high standards of historical and mathematical accuracy that were imposed on the authors of the ...

Author: Juan Tirao

Publisher: Springer Science & Business Media

ISBN: 1461241626

Category: Mathematics

Page: 326

View: 765

The representation theory of Lie groups plays a central role in both clas sical and recent developments in many parts of mathematics and physics. In August, 1995, the Fifth Workshop on Representation Theory of Lie Groups and its Applications took place at the Universidad Nacional de Cordoba in Argentina. Organized by Joseph Wolf, Nolan Wallach, Roberto Miatello, Juan Tirao, and Jorge Vargas, the workshop offered expository courses on current research, and individual lectures on more specialized topics. The present vol ume reflects the dual character of the workshop. Many of the articles will be accessible to graduate students and others entering the field. Here is a rough outline of the mathematical content. (The editors beg the indulgence of the readers for any lapses in this preface in the high standards of historical and mathematical accuracy that were imposed on the authors of the articles. ) Connections between flag varieties and representation theory for real re ductive groups have been studied for almost fifty years, from the work of Gelfand and Naimark on principal series representations to that of Beilinson and Bernstein on localization. The article of Wolf provides a detailed introduc tion to the analytic side of these developments. He describes the construction of standard tempered representations in terms of square-integrable partially harmonic forms (on certain real group orbits on a flag variety), and outlines the ingredients in the Plancherel formula. Finally, he describes recent work on the complex geometry of real group orbits on partial flag varieties.

Representations of Reductive p adic Groups

The book should be a valuable resource to graduate students and experienced researchers alike. This book consists of survey articles and original research papers in the representation theory of reductive p-adic groups.

Author: Anne-Marie Aubert

Publisher: Birkhäuser

ISBN: 9789811366277

Category: Mathematics

Page: 289

View: 286

This book consists of survey articles and original research papers in the representation theory of reductive p-adic groups. In particular, it includes a survey by Anne-Marie Aubert on the enormously influential local Langlands conjectures. The survey gives a precise and accessible formulation of many aspects of the conjectures, highlighting recent refinements, due to the author and her collaborators, and their current status. It also features an extensive account by Colin Bushnell of his work with Henniart on the fine structure of the local Langlands correspondence for general linear groups, beginning with a clear overview of Bushnell–Kutzko’s construction of cuspidal types for such groups. The remaining papers touch on a range of topics in this active area of modern mathematics: group actions on root data, explicit character formulas, classification of discrete series representations, unicity of types, local converse theorems, completions of Hecke algebras, p-adic symmetric spaces. All meet a high level of exposition. The book should be a valuable resource to graduate students and experienced researchers alike.

Unitary Representations of Exceptional P Adic Groups

that the determination of the Iwahori - spherical unitary dual for p - adic groups
can be reduced to the classification of unitary representations with real
infinitesimal character for the associated Hecke algebras and , in this setting ,
they carried ...

Author: Dan Mihai Ciubotaru

Publisher:

ISBN:

Category:

Page: 174

View: 240

One of the fundamental problems in representation theory is the classification of the irreducible unitary representations (the unitary dual) of reductive groups defined over local fields. In the case of groups over p-adic fields, an important piece of the unitary dual is formed by the Iwahori-spherical representations, which are representations with nontrivial fixed vectors under the action of a particular subgroup of G, the Iwahori subgroup.

Geometry and Representation Theory of Real and P Adic Groups

Author: Juan Tirao

Publisher:

ISBN: 9781461241638

Category:

Page: 340

View: 381


Harmonic Analysis on Reductive p adic Groups

Author: B. Harish-Chandra

Publisher: Springer

ISBN: 3540363726

Category: Mathematics

Page: 130

View: 845


Representation Theory and Analysis on Homogeneous Spaces

Combining presentation of new results with in-depth surveys of recent work, this book focuses on representation theory and harmonic analysis on real and $p$-adic groups.

Author: Simon Gindikin

Publisher: American Mathematical Soc.

ISBN: 082180300X

Category: Mathematics

Page: 256

View: 580

Combining presentation of new results with in-depth surveys of recent work, this book focuses on representation theory and harmonic analysis on real and $p$-adic groups. The papers are based on lectures presented at a conference dedicated to the memory of Larry Corwin and held at Rutgers University in February 1993. The book presents a survey of harmonic analysis on nilpotent homogeneous spaces, results on multiplicity formulas for induced representations, new methods for constructing unitary representations of real reductive groups, and a unified treatment of trace Paley-Wiener theorems for real and $p$-adic reductive groups.In the representation theory of the general linear group over $p$-adic fields, the book provides a description of Corwin's contributions, a survey of the role of Hecke algebras, and a presentation of the theory of simple types. Other types of reductive $p$-adic groups are also discussed. Among the other topics included are the representation theory of discrete rational nilpotent groups, skew-fields associated to quadratic algebras, and finite models for percolation. A timely publication featuring contributions by some of the top researchers in the field, this book offers a perspective not often found in conference proceedings.

Modular Representation Theory of Finite and p Adic Groups

This volume is an outgrowth of the program Modular Representation Theory of Finite and p-Adic Groups held at the Institute for Mathematical Sciences at National University of Singapore during the period of 1-26 April 2013.

Author: Wee Teck Gan

Publisher: World Scientific

ISBN: 9814651826

Category: Mathematics

Page: 276

View: 215

This volume is an outgrowth of the program Modular Representation Theory of Finite and p-Adic Groups held at the Institute for Mathematical Sciences at National University of Singapore during the period of 1–26 April 2013. It contains research works in the areas of modular representation theory of p-adic groups and finite groups and their related algebras. The aim of this volume is to provide a bridge — where interactions are rare between researchers from these two areas — by highlighting the latest developments, suggesting potential new research problems, and promoting new collaborations. It is perhaps one of the few volumes, if not only, which treats such a juxtaposition of diverse topics, emphasizing their common core at the heart of Lie theory. Contents:Modular Representations of Finite Reductive Groups (Marc Cabanes)ℓ-Modular Representations of p-Adic Groups (ℓ ≠ p) (Vincent Sécherre)p-Modular Representations of p-Adic Groups (Florian Herzig)Representation Theory and Cohomology of Khovanov–Lauda–Rouquier Algebras (Alexander S Kleshchev)Cyclotomic Quiver Hecke Algebras of Type A (Andrew Mathas) Readership: Graduate students and professional mathematicians interested in modular representation theory. Key Features:Contains a survey of modular representation theory of finite groups of Lie type, with a description of recent progress and outstanding conjecturesCovers the modular representation theory of p-adic groups in both defining and non-defining characteristic which is being pursued in the modular Langlands programIntroduces the increasingly popular representation theory of Khovanov–Lauda–Rouquier algebras and the graded representation theory of cyclotomic Hecke algebrasSuitable for graduate students as well as mathematical researchers who desire to learn about representation theory in these areasKeywords:Modular Representation Theory;Reductive Groups;Modular Langlands Program;Khovanov–Lauda–Rouquier Algebras;Cyclotomic Hecke Algebras

Ottawa Lectures on Admissible Representations of Reductive P adic Groups

Author: Clifton Cunningham

Publisher: American Mathematical Soc.

ISBN: 0821885944

Category: Mathematics

Page: 199

View: 841


Harish Chandra Homomorphisms for mathfrak p Adic Groups

This book introduces a systematic new approach to the construction and analysis of semisimple $p$-adic groups.

Author: Roger Howe

Publisher: American Mathematical Soc.

ISBN: 0821807099

Category: Mathematics

Page: 76

View: 740

This book introduces a systematic new approach to the construction and analysis of semisimple $p$-adic groups. The basic construction presented here provides an analogue in certain cases of the Harish-Chandra homomorphism, which has played an essential role in the theory of semisimple Lie groups. The book begins with an overview of the representation theory of GL$_n$ over finite groups. The author then explicitly establishes isomorphisms between certain convolution algebras of functions on two different groups. Because of the form of the isomorphisms, basic properties of representations are preserved, thus giving a concrete example to the correspondences predicted by the general philosphy of Langlands. The first chapter, suitable as an introduction for graduate students, requires only a basic knowledge of representation theory of finite groups and some familiarity with the general linear group and the symmetric group. The later chapters introduce researchers in the field to a new method for the explicit construction and analysis of representations of $p$-adic groups, a powerful method clearly capable of extensive further development.

Representations of Reductive Groups

This volume contains the proceedings of the Conference on Representation Theory and Algebraic Geometry, held in honor of Joseph Bernstein, from June 11–16, 2017, at the Weizmann Institute of Science and The Hebrew University of Jerusalem.

Author: Avraham Aizenbud

Publisher: American Mathematical Soc.

ISBN: 1470442841

Category: Representations of algebras

Page: 450

View: 900

This volume contains the proceedings of the Conference on Representation Theory and Algebraic Geometry, held in honor of Joseph Bernstein, from June 11–16, 2017, at the Weizmann Institute of Science and The Hebrew University of Jerusalem. The topics reflect the decisive and diverse impact of Bernstein on representation theory in its broadest scope. The themes include representations of p -adic groups and Hecke algebras in all characteristics, representations of real groups and supergroups, theta correspondence, and automorphic forms.

Harmonic Analysis on Reductive p adic Groups

Author: Robert S. Doran, Paul J. Sally, Jr., and Loren Spice

Publisher: American Mathematical Soc.

ISBN: 0821874039

Category: Harmonic analysis

Page: 277

View: 798


The Langlands Classification and Irreducible Characters for Real Reductive Groups

This book provides and introduction to some modern geometric methods in representation theory. It is addressed to graduate students and research workers in representation theory and in automorphic forms.

Author: J. Adams

Publisher: Springer Science & Business Media

ISBN: 146120383X

Category: Mathematics

Page: 320

View: 850

This monograph explores the geometry of the local Langlands conjecture. The conjecture predicts a parametrizations of the irreducible representations of a reductive algebraic group over a local field in terms of the complex dual group and the Weil-Deligne group. For p-adic fields, this conjecture has not been proved; but it has been refined to a detailed collection of (conjectural) relationships between p-adic representation theory and geometry on the space of p-adic representation theory and geometry on the space of p-adic Langlands parameters. This book provides and introduction to some modern geometric methods in representation theory. It is addressed to graduate students and research workers in representation theory and in automorphic forms.

Mathematical Reviews

Prasad , Amritanshu Almost unramified automorphic representations for split
groups over Fot ) . ( English summary ) ... p - adic groups . I . ( English summary )
2004a : 22018 - Representations modulo p of the p - adic group ... 2004e : 11051
– ( with Savin , Gordan ) Real and global lists from PGL3 to G2 . 2004k : 11079 ...

Author:

Publisher:

ISBN:

Category: Mathematics

Page:

View: 425


On the Unicity of Types for Representations of Reductive P adic Groups

Author: Peter Latham

Publisher:

ISBN:

Category:

Page:

View: 430


Arithmetical Investigations

In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers.

Author: Shai M. J. Haran

Publisher: Springer Science & Business Media

ISBN: 3540783784

Category: Mathematics

Page: 217

View: 843

In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers. The p-adic numbers contain the p-adic integers Zp which are the inverse limit of the finite rings Z/pn. This gives rise to a tree, and probability measures w on Zp correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L2(Zp,w). The real analogue of the p-adic integers is the interval [-1,1], and a probability measure w on it gives rise to a special basis for L2([-1,1],w) - the orthogonal polynomials, and to a Markov chain on "finite approximations" of [-1,1]. For special (gamma and beta) measures there is a "quantum" or "q-analogue" Markov chain, and a special basis, that within certain limits yield the real and the p-adic theories. This idea can be generalized variously. In representation theory, it is the quantum general linear group GLn(q)that interpolates between the p-adic group GLn(Zp), and between its real (and complex) analogue -the orthogonal On (and unitary Un )groups. There is a similar quantum interpolation between the real and p-adic Fourier transform and between the real and p-adic (local unramified part of) Tate thesis, and Weil explicit sums.

Notices of the American Mathematical Society

Contents O . V . Besov , Application of integral representations of functions to
interpolation of spaces of differentiable ... representation of simply laced groups ;
Marie - France Vignéras , On formal dimensions for reductive p - adic groups ; J .
- L ...

Author: American Mathematical Society

Publisher:

ISBN:

Category: Mathematics

Page:

View: 599


Mod P Representations of Reductive P adic Groups

Author: Alex Charis

Publisher:

ISBN:

Category: Algebraic number theory

Page: 28

View: 440


Representations of Reductive Groups

This volume highlights the depth and breadth of Vogan's influence over the subjects mentioned above, and point to many exciting new directions that remain to be explored.

Author: Monica Nevins

Publisher: Birkhäuser

ISBN: 9783319794839

Category: Mathematics

Page: 532

View: 749

Over the last forty years, David Vogan has left an indelible imprint on the representation theory of reductive groups. His groundbreaking ideas have lead to deep advances in the theory of real and p-adic groups, and have forged lasting connections with other subjects, including number theory, automorphic forms, algebraic geometry, and combinatorics. Representations of Reductive Groups is an outgrowth of the conference of the same name, dedicated to David Vogan on his 60th birthday, which took place at MIT on May 19-23, 2014. This volume highlights the depth and breadth of Vogan's influence over the subjects mentioned above, and point to many exciting new directions that remain to be explored. Notably, the first article by McGovern and Trapa offers an overview of Vogan's body of work, placing his ideas in a historical context. Contributors: Pramod N. Achar, Jeffrey D. Adams, Dan Barbasch, Manjul Bhargava, Cédric Bonnafé, Dan Ciubotaru, Meinolf Geck, William Graham, Benedict H. Gross, Xuhua He, Jing-Song Huang, Toshiyuki Kobayashi, Bertram Kostant, Wenjing Li, George Lusztig, Eric Marberg, William M. McGovern, Wilfried Schmid, Kari Vilonen, Diana Shelstad, Peter E. Trapa, David A. Vogan, Jr., Nolan R. Wallach, Xiaoheng Wang, Geordie Williamson

Abstracts of Papers Presented to the American Mathematical Society

Towards a lifting of representations of finite reductive groups , with applications to
p - adic base change . ... Shelstad has proven identities for real groups in the
ordinary case , and Renard has proven some twisted identities of orbital integrals
 ...

Author: American Mathematical Society

Publisher:

ISBN:

Category: Mathematics

Page:

View: 454