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© 2000

Singular Loci of Schubert Varieties

Part of the Progress in Mathematics book series (PM, volume 182)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Sara Billey, V. Lakshmibai
    Pages 1-5
  3. Sara Billey, V. Lakshmibai
    Pages 7-21
  4. Sara Billey, V. Lakshmibai
    Pages 23-36
  5. Sara Billey, V. Lakshmibai
    Pages 37-46
  6. Sara Billey, V. Lakshmibai
    Pages 47-69
  7. Sara Billey, V. Lakshmibai
    Pages 71-89
  8. Sara Billey, V. Lakshmibai
    Pages 91-102
  9. Sara Billey, V. Lakshmibai
    Pages 103-117
  10. Sara Billey, V. Lakshmibai
    Pages 119-158
  11. Sara Billey, V. Lakshmibai
    Pages 159-168
  12. Sara Billey, V. Lakshmibai
    Pages 169-173
  13. Sara Billey, V. Lakshmibai
    Pages 175-206
  14. Sara Billey, V. Lakshmibai
    Pages 207-237
  15. Back Matter
    Pages 239-251

About this book

Introduction

"Singular Loci of Schubert Varieties" is a unique work at the crossroads of representation theory, algebraic geometry, and combinatorics. Over the past 20 years, many research articles have been written on the subject in notable journals. In this work, Billey and Lakshmibai have recreated and restructured the various theories and approaches of those articles and present a clearer understanding of this important subdiscipline of Schubert varieties – namely singular loci. The main focus, therefore, is on the computations for the singular loci of Schubert varieties and corresponding tangent spaces. The methods used include standard monomial theory, the nil Hecke ring, and Kazhdan-Lusztig theory. New results are presented with sufficient examples to emphasize key points. A comprehensive bibliography, index, and tables – the latter not to be found elsewhere in the mathematics literature – round out this concise work. After a good introduction giving background material, the topics are presented in a systematic fashion to engage a wide readership of researchers and graduate students.

Keywords

Algebra and differential geometry Graph Node Representation theory combinatorics lie groups topological groups

Authors and affiliations

  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Department of MathematicsNortheastern UniversityBostonUSA

Bibliographic information

  • Book Title Singular Loci of Schubert Varieties
  • Authors Sara Sarason
    V. Lakshmibai
  • Series Title Progress in Mathematics
  • Series Abbreviated Title Progress in Mathematics(Birkhäuser)
  • DOI https://doi.org/10.1007/978-1-4612-1324-6
  • Copyright Information Birkhäuser Boston 2000
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-8176-4092-7
  • Softcover ISBN 978-1-4612-7094-2
  • eBook ISBN 978-1-4612-1324-6
  • Series ISSN 0743-1643
  • Series E-ISSN 2296-505X
  • Edition Number 1
  • Number of Pages XII, 251
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Algebraic Geometry
    Topological Groups, Lie Groups
    Combinatorics
    Differential Geometry
  • Buy this book on publisher's site

Reviews

"The authors review the major papers in the topic that have been written during the last two decades, giving a comprehensive bibliography…this is a very important survey of the subject."

-Mathematical Reviews