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Standard Monomial Theory: Invariant Theoretic Approach by V. Lakshmibai

Standard Monomial Theory: Invariant Theoretic Approach

by V. Lakshmibai
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Book cover type: Paperback
  • ISBN13: 9783642095436
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 266
  • Original Price: EUR 119.99
  • Language: English
  • Edition: N/A
  • Item Weight: 427 grams
  • BISAC Subject(s): Geometry / Algebraic and Algebra / General

From the Back Cover

Schubert varieties lie at the cross roads of algebraic geometry, combinatorics, commutative algebra, and representation theory. They are an important class of subvarieties of flag varieties, interesting in their own right, and providing an inductive tool for studying flag varieties. The literature on them is vast, for they are ubiquitous--they have been intensively studied over the last fifty years, from many different points of view and by many different authors.

This book is mainly a detailed account of a particularly interesting instance of their occurrence: namely, in relation to classical invariant theory. More precisely, it is about the connection between the first and second fundamental theorems of classical invariant theory on the one hand and standard monomial theory for Schubert varieties in certain special flag varieties - the ordinary, orthogonal, and symplectic Grassmannians - on the other. Historically, this connection was the prime motivation for the development of standard monomial theory. Determinantal varieties and basic concepts of geometric invariant theory arise naturally in establishing the connection.

The book also treats, in the last chapter, some other applications of standard monomial theory, e.g., to the study of certain naturally occurring affine algebraic varieties that, like determinantal varieties, can be realized as open parts of Schubert varieties.

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