Mathematics - Sets, General Topology, & Categories, Computer Mathematics, Mathematics - Group Theory
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Overview
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. A few topics, however, require results from the representation theory of algebraic groups; so, to keep the book reasonably self-contained, an appendix on that is included. 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.Book Details
Published
January 1, 2009
Publisher
Cambridge University Press
Pages
256
Format
Paperback
ISBN
9780521100465