**Hindustan Book Agency**

Volume: 40;
2009;
288 pp;
Hardcover

MSC: Primary 14;
**Print ISBN: 978-81-85931-92-0
Product Code: HIN/40**

List Price: $52.00

Individual Member Price: $41.60

# Flag Varieties: An Interplay of Geometry, Combinatorics, and Representation Theory

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*V. Lakshmibai; Justin Brown*

A publication of Hindustan Book Agency

Flag varieties are important geometric objects and their study involves an interplay of geometry, combinatorics, and representation theory. This book is a detailed account of this interplay. In the area of representation theory, the book discusses complex semisimple Lie algebras and semisimple algebraic groups; in addition, the representation theory of symmetric groups is discussed. In the area of algebraic geometry, the book explains in detail 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.

A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels.

#### Readership

Graduate students and research mathematicians interested in flag varieties.