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Schur Algebras and Representation Theory by Stuart Martin (Hardcover, 1994)

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Schur algebras are algebraic systems which provide a link between the representation theory of the symmetric and general linear groups (both finite and infinite). 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 also considered. The opportunity is taken to give an account of quantum versions of Schur algebras and their relations with certain q-deformations of the co-ordinate rings of general linear group. The approach is combinatorial where possible, thereby 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.