Schur Algebras and Representation Theory

Schur Algebras and Representation Theory

by Stuart Martin
     
 

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ISBN-10: 0521100461

ISBN-13: 9780521100465

Pub. Date: 01/18/2009

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:
9780521100465
Publisher:
Cambridge University Press
Publication date:
01/18/2009
Series:
Cambridge Tracts in Mathematics Series, #112
Pages:
256
Product dimensions:
6.00(w) x 8.90(h) x 0.80(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.

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