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9780821839249

Representations of Algebraic Groups, Quantum Groups, and Lie Algebras

by ; ; ; ;
  • ISBN13:

    9780821839249

  • ISBN10:

    0821839241

  • Format: Paperback
  • Copyright: 2006-10-06
  • Publisher: Amer Mathematical Society

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Summary

The book contains several well-written accessible survey papers in many interrelated areas of current research. These areas cover various aspects of the representation theory of Lie algebras, finite groups of Lie types, Hecke algebras, and Lie superalgebras. Geometric methods have been instrumental in representation theory, and the proceedings include surveys on geometric as well as combinatorial constructions of the crystal basis for representations of quantum groups. Humphreys' paper outlines intricate connections among irreducible representations of certain blocks of reduced enveloping algebras of semi-simple Lie algebras in positive characteristic left cells in two sided cells of affine Weyl groups, and the geometry of the nilpotent orbits. All these papers provide the reader with a broad picture of the interaction of many different research areas and should be helpful to those who want to have a glimpse of current research involving representation theory.

Table of Contents

Extensions for finite groups of Lie type II: Filtering the truncated induction functor
Algebras, representations and their derived categories over finite fields
On localization of $\bar D$-modules
Representations of reduced enveloping algebras and cells in the affine Weyl group
Nakajima's monomials and crystal bases
A new Lie bialgebra structure on $sl(2,1)$
The Steinberg tensor product theorem for $GL(m
Cyclotomic $q$-Schur algebras and Schur-Weyl duality
Geometric crystals and affine crystals
Self-extensions for finite symplectic groups via algebraic groups
Classification of finite dimensional simple Lie algebras in prime characteristics
From quantum groups to unitary modular tensor categories
A trip from representations of the Kronecker quiver to canonical bases of quantum affine algebras
Table of Contents provided by Publisher. All Rights Reserved.

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