Representation Theory of Reductive Groups
| Author | : Peter C. Trombi |
| Publisher | : |
| Total Pages | : 320 |
| Release | : 1983 |
| Genre | : Representations of groups |
| ISBN | : |
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Representation Theory of Finite Reductive Groups
| Author | : Marc Cabanes |
| Publisher | : Cambridge University Press |
| Total Pages | : 457 |
| Release | : 2004-01-29 |
| Genre | : Mathematics |
| ISBN | : 0521825172 |
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Publisher Description
Representations of Algebraic Groups
| Author | : Jens Carsten Jantzen |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 594 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 082184377X |
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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.
Representations of Reductive Groups
| Author | : Roger W. Carter |
| Publisher | : Cambridge University Press |
| Total Pages | : 203 |
| Release | : 1998-09-03 |
| Genre | : Mathematics |
| ISBN | : 0521643252 |
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This volume provides a very accessible introduction to the representation theory of reductive algebraic groups.
Representations of Reductive Groups
| Author | : Monica Nevins |
| Publisher | : Birkhäuser |
| Total Pages | : 0 |
| Release | : 2016-01-06 |
| Genre | : Mathematics |
| ISBN | : 9783319234427 |
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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
Unitary Representations of Reductive Lie Groups. (AM-118), Volume 118
| Author | : David A. Vogan Jr. |
| Publisher | : Princeton University Press |
| Total Pages | : 319 |
| Release | : 2016-03-02 |
| Genre | : Mathematics |
| ISBN | : 1400882389 |
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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.
Introduction to Representation Theory
| Author | : Pavel I. Etingof |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 240 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 0821853511 |
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Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.
Algebraic and Analytic Methods in Representation Theory
| Author | : |
| Publisher | : Elsevier |
| Total Pages | : 357 |
| Release | : 1996-09-27 |
| Genre | : Mathematics |
| ISBN | : 0080526950 |
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This book is a compilation of several works from well-recognized figures in the field of Representation Theory. The presentation of the topic is unique in offering several different points of view, which should makethe book very useful to students and experts alike. Presents several different points of view on key topics in representation theory, from internationally known experts in the field
The Langlands Classification and Irreducible Characters for Real Reductive Groups
| Author | : J. Adams |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 331 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 146120383X |
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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.
Real Reductive Groups I
| Author | : Nolan R. Wallach |
| Publisher | : Academic Press |
| Total Pages | : 439 |
| Release | : 1988-03-01 |
| Genre | : Mathematics |
| ISBN | : 0080874517 |
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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.
