Flag Varieties

An Interplay of Geometry, Combinatorics, and Representation Theory

  • V. Lakshmibai
  • Justin Brown

Part of the Texts and Readings in Mathematics book series (TRIM, volume 53)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. V. Lakshmibai, Justin Brown
    Pages 1-23
  3. V. Lakshmibai, Justin Brown
    Pages 25-46
  4. V. Lakshmibai, Justin Brown
    Pages 47-58
  5. V. Lakshmibai, Justin Brown
    Pages 59-82
  6. V. Lakshmibai, Justin Brown
    Pages 83-93
  7. V. Lakshmibai, Justin Brown
    Pages 107-122
  8. V. Lakshmibai, Justin Brown
    Pages 123-136
  9. V. Lakshmibai, Justin Brown
    Pages 137-160
  10. V. Lakshmibai, Justin Brown
    Pages 161-181
  11. V. Lakshmibai, Justin Brown
    Pages 183-196
  12. V. Lakshmibai, Justin Brown
    Pages 225-231
  13. V. Lakshmibai, Justin Brown
    Pages 233-243
  14. Back Matter
    Pages 245-274

About this book

Introduction

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.

Authors and affiliations

  • V. Lakshmibai
    • 1
  • Justin Brown
    • 1
  1. 1.Northeastern UniversityBostonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-93-86279-41-5
  • Copyright Information Hindustan Book Agency (India) 2009
  • Publisher Name Hindustan Book Agency, Gurgaon
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-81-85931-92-0
  • Online ISBN 978-93-86279-41-5
  • Series Print ISSN 2366-8717
  • Series Online ISSN 2366-8725
  • About this book