Schur Algebras and Representation Theory

Schur Algebras and Representation Theory

by Stuart Martin, Martin Stuart
     
 

View All Available Formats & Editions

ISBN-10: 0521415918

ISBN-13: 9780521415910

Pub. Date: 02/28/2007

Publisher: Cambridge University Press

Schur algebras are an algebraic system that provide a link between the representation theory of the symmetric and general linear groups. Dr. Martin gives a self-contained account of this algebra and those links, covering the basic ideas and their quantum analogues. He discusses not only the usual representation-theoretic topics (such as constructions of irreducible

Overview

Schur algebras are an algebraic system that provide a link between the representation theory of the symmetric and general linear groups. Dr. Martin gives a self-contained account of this algebra and those links, covering the basic ideas and their quantum analogues. He discusses not only the usual representation-theoretic topics (such as constructions of irreducible modules, the structure of blocks containing them, decomposition numbers and so on) but also the intrinsic properties of Schur algebras, leading to a discussion of their cohomology theory. He also investigates the relationship between Schur algebras and other algebraic structures. Throughout, the approach uses combinatorial language where possible, thereby making the presentation accessible to graduate students. Some topics require results from algebraic group theory, which are contained in an appendix.

Product Details

ISBN-13:
9780521415910
Publisher:
Cambridge University Press
Publication date:
02/28/2007
Series:
Cambridge Tracts in Mathematics Series, #112
Pages:
252
Product dimensions:
5.98(w) x 8.98(h) x 0.67(d)

Table of Contents

Introduction; 1. Polynomial functions and combinatorics; 2. The Schur algebra; 3. Representation theory of the Schur algebra; 4. Schur functors and the symmetric group; 5. Block theory; 6. The q-Schur algebra; 7. Representation theory of Sq (n, r); Appendix: a review of algebraic groups; References; Indexes.

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >