Cambridge Tracts in Mathematics: Linear and Projective Representations of Symmetric Groups (Volume 163)

Kleshchev, Alexander

ISBN 10: 0521837030 / ISBN 13: 9780521837033

Published by Cambridge University Press, 2005

About this Item

Volume 163. This is an ex-library book and may have the usual library/used-book markings inside.This book has hardback covers. In good all round condition. No dust jacket. Please note the Image in this listing is a stock photo and may not match the covers of the actual item,600grams, ISBN:0521837030.

Seller Inventory # 5763819

Bibliographic Details

• Title: Cambridge Tracts in Mathematics: Linear and Projective Representations of Symmetric Groups (Volume 163)
• Publisher: Cambridge University Press
• Publication Date: 2005
• Language: English
• ISBN 10: 0521837030
• ISBN 13: 9780521837033
• Binding: Hardcover
• Condition: Good
• Weight: 600 grams
• Seller catalogs:
  • Mathematics

About this title

Synopsis

The representation theory of symmetric groups is one of the most beautiful, popular, and important parts of algebra with many deep relations to other areas of mathematics, such as combinatorics, Lie theory, and algebraic geometry. Kleshchev describes a new approach to the subject, based on the recent work of Lascoux, Leclerc, Thibon, Ariki, Grojnowski, Brundan, and the author. Much of this work has only appeared in the research literature before. However, to make it accessible to graduate students, the theory is developed from scratch, the only prerequisite being a standard course in abstract algebra. Branching rules are built in from the outset resulting in an explanation and generalization of the link between modular branching rules and crystal graphs for affine Kac-Moody algebras. The methods are purely algebraic, exploiting affine and cyclotomic Hecke algebras. For the first time in book form, the projective (or spin) representation theory is treated along the same lines as linear representation theory. The author is mainly concerned with modular representation theory, although everything works in arbitrary characteristic, and in case of characteristic 0 the approach is somewhat similar to the theory of Okounkov and Vershik, described here in chapter 2. For the sake of transparency, Kleshschev concentrates on symmetric and spin-symmetric groups, though the methods he develops are quite general and apply to a number of related objects. In sum, this unique book will be welcomed by graduate students and researchers as a modern account of the subject.

About the Author

Alexander Kleshchev is a Professor of Mathematics at the University of Oregon.