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Introduction to the Theory of Standard Monomials

Second Edition

  • C. S. Seshadri

Part of the Texts and Readings in Mathematics book series (TRIM, volume 46)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. C. S. Seshadri
    Pages 1-53
  3. C. S. Seshadri
    Pages 55-80
  4. C. S. Seshadri
    Pages 81-105
  5. C. S. Seshadri
    Pages 107-137
  6. Back Matter
    Pages 139-224

About this book

Introduction

The book is a reproduction of a course of lectures delivered 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 standard monomial theory due to the work of Peter Littelmann. The author’s lectures (reproduced in this book) remain an excellent introduction to standard monomial theory.

d-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;">Standard monomial theory 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 with these groups. Besides its intrinsic interest, standard monomial theory has applications to the study of the geometry of Schubert varieties. Standard monomial theory 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, standard monomial theory was developed by the author in a series of papers written in collaboration with V. Lakshmibai and C. Musili. In the second edition of the book, conjectures of a standard monomial theory for a general semi-simple (simply-connected) algebraic group, due to Lakshmibai, have been added as an appendix, and the bibliography has been revised.

Keywords

Grassmannian Plucker coordinates Schubert varieties Standard monomials Vanishing theorem Deodhar’s Lemma

Authors and affiliations

  • C. S. Seshadri
    • 1
  1. 1.Chennai Mathematical InstituteChennaiIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-10-1813-8
  • Copyright Information Springer Science+Business Media Singapore 2016
  • Publisher Name Springer, Singapore
  • eBook Packages Mathematics and Statistics
  • Online ISBN 978-981-10-1813-8
  • Series Print ISSN 2366-8717
  • Series Online ISSN 2366-8725
  • Buy this book on publisher's site