Linear and Projective Representations of Symmetric Groups (Cambridge Tracts in Mathematics, Series Number 163) - Hardcover

Kleshchev, Alexander

Hardcover

ISBN 10: 0521837030 ISBN 13: 9780521837033

Publisher: Cambridge University Press, 2005

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 this title

Book Description

The representation theory of the symmetric group is of perennial interest since it touches on so many areas of mathematics. This book contains some of the modern theory, to which the author was one of the main contributors. He brings the reader right up to the frontiers of the subject in a work which will be an invaluable resource for graduate students and researchers.

About the Author

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

Edition details

• Publisher: Cambridge University Press
• Publication date: 2005
• ISBN 10: 0521837030
• ISBN 13: 9780521837033
• Binding: Hardcover
• Language: English
• Number of pages: 292