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Item Details
Title: FLAG VARIETIES
AN INTERPLAY OF GEOMETRY, COMBINATORICS, AND REPRESENTATION THEORY
By: V. Lakshmibai, Justin Brown
Format: Hardback

List price: £49.95


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ISBN 10: 8185931925
ISBN 13: 9788185931920
Publisher: HINDUSTAN BOOK AGENCY
Pub. date: 15 January, 2009
Series: Texts and Readings in Mathematics v. 53
Pages: 288
Description: Flag varieties are important geometric objects and their study involves an interplay of geometry, combinatorics, and representation theory. This book details an account of this interplay. It discusses complex semisimple Lie algebras and of semisimple algebraic groups; as well as, the representation theory of symmetric groups.
Synopsis: Flag varieties are important geometric objects and their study involves an interplay of geometry, combinatorics, and representation theory. This book is detailed account of this interplay. In the area of representation theory, the book presents a discussion of complex semisimple Lie algebras and of semisimple algebraic groups; in addition, the representation theory of symmetric groups is also discussed. In the area of algebraic geometry, the book gives a detailed account of the Grassmannian varieties, flag varieties, and their Schubert subvarieties. Because of the connections with root systems, many of the geometric results admit elegant combinatorial description, a typical example being the description of the singular locus of a Schubert variety. This is shown to be a consequence of standard monomial theory (abbreviated SMT). Thus the book includes SMT and some important applications - singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory.
Publication: India
Imprint: Hindustan Book Agency
Returns: Returnable
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