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

V. Lakshmibai

ISBN 10: 9386279703 / ISBN 13: 9789386279705

Published by Jainendra K Jain, 1905

About this Item

2018. 2nd Revised edition. Hardcover. . . . . . Books ship from the US and Ireland.

Seller Inventory # V9789386279705

Bibliographic Details

• Title: Flag Varieties: An Interplay of Geometry, Combinatorics, and Representation Theory (Hindustan Book Agency)
• Publisher: Jainendra K Jain
• Publication Date: 1905
• Language: English
• ISBN 10: 9386279703
• ISBN 13: 9789386279705
• Binding: Hardcover
• Edition: 2nd Edition
• Condition: New

About this title

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.