Schur Algebras and Representation Theory [Paperback]

This is the first comprehensive text in this important and active area of research.The Schur algebra is an algebraic system providing a link between the representation theory of the symmetric and general linear groups. The approach is combinatorial where possible, making the presentation accessible to graduate students. 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.The Schur algebra is an algebraic system providing a link between the representation theory of the symmetric and general linear groups. The approach is combinatorial where possible, making the presentation accessible to graduate students. 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.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.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, rl#•