Schur algebras and representation theory
By: Stuart Martin.
Series: Cambridge tracts in mathematics ;; 112
Publisher: Cambridge University Press
Published: 1993
Place of publication: Cambridge
Language: eng
Number of pages: 232
Subjects: Representations of groups.; Representations of algebras.
Description: 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.
Notes: Includes bibliographical references (p. 220-226) and index.