Name: standard monomial theory
SKU: 3432369
Price: 3915.00 TWD
Availability: InStock
Author: lakshmibai,raghavan
ISBN: 9783540767565

Type

Physical Book

Publisher

Springer

Author

lakshmibai,raghavan

Language

English

Pages

266

ISBN

3540767568

ISBN13

9783540767565

Synopsis "standard monomial theory"

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.