Schur Algebras and Representation Theoryby Stuart Martin
Pub. Date: 01/18/2009
Publisher: Cambridge University Press
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.
Table of ContentsIntroduction; 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.
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