Overview
- Authors:
-
-
V. Lakshmibai
-
Northeastern University, Boston, USA
-
Justin Brown
-
Northeastern University, Boston, USA
Access this book
Other ways to access
Table of contents (14 chapters)
-
-
- V. Lakshmibai, Justin Brown
Pages 1-23
-
- V. Lakshmibai, Justin Brown
Pages 25-46
-
- V. Lakshmibai, Justin Brown
Pages 47-58
-
- V. Lakshmibai, Justin Brown
Pages 59-82
-
- V. Lakshmibai, Justin Brown
Pages 83-93
-
- V. Lakshmibai, Justin Brown
Pages 95-105
-
- V. Lakshmibai, Justin Brown
Pages 107-122
-
- V. Lakshmibai, Justin Brown
Pages 123-136
-
- V. Lakshmibai, Justin Brown
Pages 137-160
-
- V. Lakshmibai, Justin Brown
Pages 161-181
-
- V. Lakshmibai, Justin Brown
Pages 183-196
-
- V. Lakshmibai, Justin Brown
Pages 197-223
-
- V. Lakshmibai, Justin Brown
Pages 225-231
-
- V. Lakshmibai, Justin Brown
Pages 233-243
-
Back Matter
Pages 245-274
About this book
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.
