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: Flag Varieties
    sub title: An Interplay of Geometry, Combinatorics, and Representation Theory
  name:
    name part: Lakshmibai, V.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Brown, Justin.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xx
    date issued: 2009
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: 286 p. online resource.
  abstract: 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.
  note: by V. Lakshmibai, Justin Brown.
  subject:
    topic: Mathematics
  subject:
    topic: Mathematics
  subject:
    topic: Mathematics, general
  classification: QA1-939
  classification: 510
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Texts and Readings in Mathematics, 53
  identifier: 9789386279415
  identifier: http://dx.doi.org/10.1007/978-93-86279-41-5
  record info:
    record creation date: 170720
    record change date: 20170720090631.0
    record identifier: 978-93-86279-41-5