Schur Algebras and Representation Theory by Stuart Martin (English) Paperback Bo

Publisher 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. 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.

Author Biography

Stuart Martin was named one of the Readeras Digest young illustrators of the year during his Cambridge student years, but held a variety of design jobs before finally becoming a childrenas book illustrator. He painted teddy bears on antique furniture reproductions and created murals for pubs, clubs, hotels, and childrenas play areas, but has concentrated on juvenile books for the past 12 years. He lives in Burton on Trent, England.

Table of Contents

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, r); Appendix: a review of algebraic groups; References; Indexes.

Review

"this book can be a source of useful information for beginners in the field of representations of symmetric and general linear groups and finite-dimensional algebras and specialists as well. Most of the treatments are combinatorial, so it is accessible to graduate students...the text is comprehensible and the research area is important and active...the book is readable and will be a handy book for specialists whose interests lie in this area." Jie Du, Mathematical Reviews "An excellent and thorough survey of one of the currently liveliest topics in algebra. Congratulations for work well done, Mr, Martin." The Bulletin of Mathematics

Review Quote

"this book can be a source of useful information for beginners in the field of representations of symmetric and general linear groups and finite-dimensional algebras and specialists as well. Most of the treatments are combinatorial, so it is accessible to graduate students...the text is comprehensible and the research area is important and active...the book is readable and will be a handy book for specialists whose interests lie in this area." Jie Du, Mathematical Reviews

Promotional "Headline"

This is the first comprehensive text in this important and active area of research.

Description for Bookstore

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.

Description for Library

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.

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