Representation Theories and Algebraic Geometry / Edition 1

by A. Broer, Gert Sabidussi

Overview

The 12 lectures presented in Representation Theories and Algebraic Geometry focus on the very rich and powerful interplay between algebraic geometry and the representation theories of various modern mathematical structures, such as reductive groups, quantum groups, Hecke algebras, restricted Lie algebras, and their companions. This interplay has been extensively exploited during recent years, resulting in great progress in these representation theories. Conversely, a great stimulus has been given to the development of such geometric theories as D-modules, perverse sheafs and equivariant intersection cohomology.
The range of topics covered is wide, from equivariant Chow groups, decomposition classes and Schubert varieties, multiplicity free actions, convolution algebras, standard monomial theory, and canonical bases, to annihilators of quantum Verma modules, modular representation theory of Lie algebras and combinatorics of representation categories of Harish-Chandra modules.

Product Details

ISBN-13:	9789048150755
Publisher:	Springer Netherlands
Publication date:	12/10/2010
Series:	Nato Science Series C: , #514
Edition description:	Softcover reprint of hardcover 1st ed. 1998
Pages:	444
Product dimensions:	6.30(w) x 9.45(h) x 0.04(d)

Table of Contents

Equivariant cohomology and equivariant intersection theory.- Lectures on decomposition classes.- Instantons and Kähler geometry of nilpotent orbits.- Geometric methods in the representation theory of Hecke algebras and quantum groups.- Representations of Lie algebras in prime characteristic.- Sur l’annulateur d’un module de Verma.- Some remarks on multiplicity free spaces.- Standard Monomial Theory and applications.- Canonical bases and Hall algebras.- Combinatorics of Harish-Chandra modules.- Schubert varieties and generalizations.

Editorial Reviews

Proceedings of a summer 1997 meeting, dealing with the interaction between various representation theories and algebraic geometry. Topics discussed include equivariant cohomology and intersection theory, decomposition classes, multiplicity free spaces, representations of Lie algebras in prime characteristic, standard monomial theory and applications, canonical bases and Hall algebras, combinatorics of Harish-Chandra modules, geometric methods in the representation theory of Hecke algebras and quantum groups, and Schubert generalizations. Annotation c. by Book News, Inc., Portland, Or.

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