Linear and projective representations of symmetric groups
By: Alexander Kleshchev.
Series: Cambridge tracts in mathematics ;; 163
Publisher: Cambridge University Press
Published: 2005
Place of publication: Cambridge, U.K; New York
Language: eng
Number of pages: 277
Subjects: Representations of groups.; Symmetry groups.; Modular representations of groups.; Hecke algebras.; Superalgebras.; Linear algebraic groups.; Algebras, Linear.; Geometry, Projective.
Description: 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 combinatories, Lie theory and algebraic geometry. 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. Much of this work has previously appeared only in the research literature. However to make it accessible to graduate students, the theory is developed from scratch, the only prerequisite being a standard course in abstract algebra. For the sake of transparency, Kleshchev concentrates on symmetric and spin-symmetric groups, though 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.
Notes: Includes bibliographical references (p. 270-274) and index.