rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Introduction to the Theory of Standard Monomials
    sub title: Second Edition
  name:
    name part: Seshadri, C. S.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: si
    date issued: 2016
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVI, 224 p. 20 illus. online resource.
  abstract: 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.
  table of contents: Chapter 1. Schubert Varieties in the Grassmannian -- Chapter 2. Standard monomial theory on SLn(k)/Q -- Chapter 3. Applications -- Chapter 4. Schubert varieties in G/Q.
  note: by C. S. Seshadri.
  subject:
    topic: Mathematics
  subject:
    topic: Algebraic geometry
  subject:
    topic: Algebra
  subject:
    topic: Field theory (Physics)
  subject:
    topic: Mathematics
  subject:
    topic: Algebraic Geometry
  subject:
    topic: Field Theory and Polynomials
  classification: QA564-609
  classification: 516.35
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Texts and Readings in Mathematics, 46
  identifier: 9789811018138
  identifier: http://dx.doi.org/10.1007/978-981-10-1813-8
  record info:
    record creation date: 160822
    record change date: 20160822130414.0
    record identifier: 978-981-10-1813-8