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Representations of Algebraic Groups

Jens Carsten Jantzen
Representations of Algebraic Groups by Jens Carsten Jantzen PDF

Author : Jens Carsten Jantzen
Publisher : American Mathematical Soc.
Page : 594 pages
File Size : 41,37 MB
Release : 2003
Category : 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.

Varieties of Representations of Finitely Generated Groups

Alexander Lubotzky
Varieties of Representations of Finitely Generated Groups by Alexander Lubotzky PDF

Author : Alexander Lubotzky
Publisher : American Mathematical Soc.
Page : 134 pages
File Size : 12,46 MB
Release : 1985
Category : Mathematics
ISBN : 082182337X

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The n-dimensional representations, over an algebraically closed characteristic zero field k, of a finitely generated group are parameterized by an affine algebraic variety over k. The tangent spaces of this variety are subspaces of spaces of one-cocycles and thus the geometry of the variety is locally related to the cohomology of the group. The cohomology is also related to the prounipotent radical of the proalgebraic hull of the group. This paper exploits these two relations to compute dimensions of representation varieties, especially for nilpotent groups and their generalizations. It also presents the foundations of the theory of representation varieties in an expository, self-contained manner.

Algebraic Groups

J. S. Milne
Algebraic Groups by J. S. Milne PDF

Author : J. S. Milne
Publisher : Cambridge University Press
Page : 665 pages
File Size : 33,95 MB
Release : 2017-09-21
Category : Mathematics
ISBN : 1107167485

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Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.

Representations of Real and P-adic Groups

Eng-chye Tan
Representations of Real and P-adic Groups by Eng-chye Tan PDF

Author : Eng-chye Tan
Publisher : World Scientific
Page : 426 pages
File Size : 21,44 MB
Release : 2004
Category : Science
ISBN : 981238779X

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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.

Introduction to Representation Theory

Pavel I. Etingof
Introduction to Representation Theory by Pavel I. Etingof PDF

Author : Pavel I. Etingof
Publisher : American Mathematical Soc.
Page : 240 pages
File Size : 35,86 MB
Release : 2011
Category : 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.