Schur Algebras and Representation Theory

This is the first comprehensive text in this important and active area of research.

Stuart Martin (Author)

9780521415910, Cambridge University Press

Hardback, published 27 January 1994

252 pages
22.9 x 15.2 x 1.7 cm, 0.48 kg

"An excellent and thorough survey of one of the currently liveliest topics in algebra. Congratulations for work well done, Mr, Martin." The Bulletin of Mathematics

The Schur algebra is an algebraic system providing a link between the representation theory of the symmetric and general linear groups (both finite and infinite). In the text Dr Martin gives a full, self-contained account of this algebra and these links, covering both the basic theory of Schur algebras and related areas. He discusses the usual representation-theoretic topics such as constructions of irreducible modules, the blocks containing them, their modular characters and the problem of computing decomposition numbers; moreover deeper properties such as the quasi-hereditariness of the Schur algebra are discussed. The opportunity is taken to give an account of quantum versions of Schur algebras and their relations with certain q-deformations of the coordinate rings of the general linear group. The approach is combinatorial where possible, making the presentation accessible to graduate students. This is the first comprehensive text in this important and active area of research; it will be of interest to all research workers in representation theory.

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.

Subject Areas: Algebra [PBF]