Linear and Projective Representations of Symmetric Groups [Paperback]

Kleshchev describes a new approach to the subject of the representation theory of symmetric groups.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.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.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 oflƒ*