Representations Of Linear Groups

Linear Representations of Finite Groups

Groups and Representations

The aim of this book is to provide a concise treatment of some topics from group theory and representation theory for a one term course. It focuses on the non-commutative side of the field emphasizing the general linear group as the most important group and example. The book will enable graduate students from every mathematical field, as well as strong undergraduates with an interest in algebra, to solidify their knowledge of group theory. The reader should have a familiarity with groups, rings, and fields, along with a solid knowledge of linear algebra. Close to 200 exercises of varying difficulty serve both to reinforce the main concept of the text and to expose the reader to additional topics.

Linear and Projective Representations of Symmetric Groups

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. Kleshchev describes a new approach to the subject, based on the recent work of Lascoux, Leclerc, Thibon, Ariki, Grojnowski and Brundan, as well as his own