Synopses & Reviews
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.
Synopsis
The only comprehensive and up-to-date treatment of Schur algebras and their quantum analogues. Suitable for researchers in algebra.
Synopsis
Dr Martin covers the basic ideas of classical Schur algebras and their quantum analogues. He discusses not only the usual representation-theoretic topics but also their intrinsic properties, leading to a discussion of their cohomology theory. The opportunity is also taken to investigate 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. This is the first comprehensive text in this important and active area of research; it will interest all working in representation theory.
Synopsis
This study is a comprehensive treatment of Schur algebras and their quantum analogues.
Synopsis
This is the first comprehensive text in this important and active area of research.
Description
Includes bibliographical references (p. 220-226) and index.
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; Index of notation; Index of terms.