Flag Varieties: An Interplay of Geometry, Combinatorics, and Representation Theory (Hindustan Book Agency) - Hardcover

V. Lakshmibai (author) & Justin Brown (author)

Hardcover

ISBN 10: 9386279703 ISBN 13: 9789386279705

Publisher: Hindustan Book Agency, 2018

Synopsis

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 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 Grassmann varieties, flag varieties, and their Schubert subvarieties. Because of their 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.

In this second edition, two recent results on Schubert varieties in the Grassmannian have been added, and some errors in the first edition corrected.

Edition details

• Publisher: Hindustan Book Agency
• Publication date: 2018
• Language: English
• ISBN 10: 9386279703
• ISBN 13: 9789386279705
• Binding: Hardcover
• Edition number: 2
• Number of pages: 325