Author : Jens Carsten Jantzen
Publisher : American Mathematical Soc.
Page : 594 pages
File Size : 18,47 MB
Release : 2003
Category : Mathematics
ISBN : 082184377X
Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.
Author : Monica Nevins
Publisher : Birkhäuser
Page : 0 pages
File Size : 11,7 MB
Release : 2016-01-06
Category : Mathematics
ISBN : 9783319234427
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
Author : Roger W. Carter
Publisher : Cambridge University Press
Page : 203 pages
File Size : 44,83 MB
Release : 1998-09-03
Category : Mathematics
ISBN : 0521643252
This volume provides a very accessible introduction to the representation theory of reductive algebraic groups.
Author : David A. Vogan Jr.
Publisher : Princeton University Press
Page : 319 pages
File Size : 46,37 MB
Release : 2016-03-02
Category : Mathematics
ISBN : 1400882389
This book is an expanded version of the Hermann Weyl Lectures given at the Institute for Advanced Study in January 1986. It outlines some of what is now known about irreducible unitary representations of real reductive groups, providing fairly complete definitions and references, and sketches (at least) of most proofs. The first half of the book is devoted to the three more or less understood constructions of such representations: parabolic induction, complementary series, and cohomological parabolic induction. This culminates in the description of all irreducible unitary representation of the general linear groups. For other groups, one expects to need a new construction, giving "unipotent representations." The latter half of the book explains the evidence for that expectation and suggests a partial definition of unipotent representations.
Author : Marc Cabanes
Publisher : Cambridge University Press
Page : 457 pages
File Size : 20,33 MB
Release : 2004-01-29
Category : Mathematics
ISBN : 0521825172
Publisher Description
Author : Peter C. Trombi
Publisher :
Page : 320 pages
File Size : 29,43 MB
Release : 1983
Category : Representations of groups
ISBN :
Author : Nolan R. Wallach
Publisher : Academic Press
Page : 439 pages
File Size : 44,50 MB
Release : 1988-03-01
Category : Mathematics
ISBN : 0080874517
Real Reductive Groups I is an introduction to the representation theory of real reductive groups. It is based on courses that the author has given at Rutgers for the past 15 years. It also had its genesis in an attempt of the author to complete a manuscript of the lectures that he gave at the CBMS regional conference at The University of North Carolina at Chapel Hill in June of 1981. This book comprises 10 chapters and begins with some background material as an introduction. The following chapters then discuss elementary representation theory; real reductive groups; the basic theory of (g, K)-modules; the asymptotic behavior of matrix coefficients; The Langlands Classification; a construction of the fundamental series; cusp forms on G; character theory; and unitary representations and (g, K)-cohomology. This book will be of interest to mathematicians and statisticians.
Author : Yves Benoist
Publisher : Springer
Page : 319 pages
File Size : 26,81 MB
Release : 2016-10-20
Category : Mathematics
ISBN : 3319477218
The classical theory of random walks describes the asymptotic behavior of sums of independent identically distributed random real variables. This book explains the generalization of this theory to products of independent identically distributed random matrices with real coefficients. Under the assumption that the action of the matrices is semisimple – or, equivalently, that the Zariski closure of the group generated by these matrices is reductive - and under suitable moment assumptions, it is shown that the norm of the products of such random matrices satisfies a number of classical probabilistic laws. This book includes necessary background on the theory of reductive algebraic groups, probability theory and operator theory, thereby providing a modern introduction to the topic.
Author : Armand Borel
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 49,72 MB
Release : 1979-06-30
Category : Mathematics
ISBN : 0821814370
Part 2 contains sections on Automorphic representations and $L$-functions, Arithmetical algebraic geometry and $L$-functions
Author : J. Adams
Publisher : Springer Science & Business Media
Page : 331 pages
File Size : 40,3 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 146120383X
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.
