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Introduction to the Theory of Standard Monomials: Second Edition
C. S. Seshadri, Chennai Mathematical Institute, Tamil Nadu, India
A publication of Hindustan Book Agency.
cover
Hindustan Book Agency
2014; 236 pp; softcover
ISBN-10: 93-80250-42-8
ISBN-13: 978-93-80250-42-7
List Price: US$48
Institutional Members: US$38.40
All Individuals: US$38.40
Order Code: HIN/34.R
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The aim of this book is to give an introduction to what has come to be known as Standard Monomial Theory (SMT). SMT deals with the construction of nice bases of finite dimensional irreducible representations of semi-simple algebraic groups or, in geometric terms, nice bases of coordinate rings of flag varieties (and their Schubert subvarieties) associated to these groups. Besides its intrinsic interest, SMT has applications to the study of the geometry of Schubert varieties. SMT has its origin in the work of Hodge, giving bases of the coordinate rings of the Grassmannian and its Schubert subvarieties by "standard monomials". In its modern form, SMT was developed by the author in a series of papers written in collaboration with V. Lakshmibai and C. Musili.

This book is a reproduction of a course of lectures given by the author in 1983-84 which appeared in the Brandeis Lecture Notes series. The aim of this course was to give an introduction to the series of papers by concentrating on the case of the full linear group. In recent years, there has been great progress in SMT due to the work of Peter Littelmann. Seshadri's course of lectures (reproduced in this book) remains an excellent introduction to SMT.

In this edition, Conjectures of a Standard Monomial Theory (SMT) for a general semi-simple (simply-connected) algebraic group, due to Lakshmibai, have been added as Appendix C. Many typographical errors have been corrected, and the bibliography has been revised.

A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels.

Readership

Graduate students and research mathematicians interested in algebra and algebraic geometry.

Table of Contents

  • Introduction
  • Schubert varieties in the Grassmannian
  • Standard monomial theory on \(\mathrm{SL}_n (k)/Q\)
  • Applications
  • Schubert varieties in \(G/Q\)
  • Appendix A. Cohen-Macaulay Properties
  • Appendix B. Normality of Schubert varieties
  • Appendix C. Standard monomial theory
  • Bibliography
  • Notation
  • Index
  • Symbols
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