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Flag Varieties

An Interplay of Geometry, Combinatorics, and Representation Theory

Summary

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.


Author: V. Lakshmibai,Justin Brown
Year: 2009
Price: Rs. 450
Binding: Hardcover
Pages: 288
Dimensions: 9.5 in x 6.5 in x 0.9 in
Publisher: Hindustan Book Agency
Sales Restriction: Sale in India & Sri Lanka Only.
ISBN 13: 9788185931920

Category:
Author Information & Reviews Mathematics


Table of contents
Table of contents

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