Texts and Readings in Mathematics

Flag Varieties

An Interplay of Geometry, Combinatorics, and Representation Theory

Authors: Lakshmibai, V.

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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.

Table of contents (14 chapters)

Table of contents (14 chapters)

Buy this book

eBook $48.00
price for USA in USD
  • ISBN 978-93-86279-41-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Flag Varieties
Book Subtitle
An Interplay of Geometry, Combinatorics, and Representation Theory
Authors
Series Title
Texts and Readings in Mathematics
Series Volume
53
Copyright
2009
Publisher
Hindustan Book Agency
Copyright Holder
Hindustan Book Agency (India)
eBook ISBN
978-93-86279-41-5
DOI
10.1007/978-93-86279-41-5
Edition Number
1
Number of Pages
286
Topics