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＜電子ブック＞
Standard Monomial Theory : Invariant Theoretic Approach / by V. Lakshmibai, K. N. Raghavan
(Encyclopaedia of Mathematical Sciences ; 137)

版	1st ed. 2008.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2008
本文言語	英語
大きさ	XIV, 266 p : online resource
著者標目	*Lakshmibai, V author Raghavan, K. N author SpringerLink (Online service)
件　名	LCSH:Algebraic geometry LCSH:Algebra FREE:Algebraic Geometry FREE:Algebra
一般注記	Generalities on algebraic varieties -- Generalities on algebraic groups -- Grassmannian -- Determinantal varieties -- Symplectic Grassmannian -- Orthogonal Grassmannian -- The standard monomial theoretic basis -- Review of GIT -- Invariant theory -- SLn(K)-action -- SOn(K)-action -- Applications of 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 HTTP:URL=https://doi.org/10.1007/978-3-540-76757-2

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