Standard monomial theory : invariant theoretic approach
著者
書誌事項
Standard monomial theory : invariant theoretic approach
（Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze, v. 137 . Invariant theory and algebraic transformation groups ; 8）
Springer, c2008
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注記
Bibliography: p. [243]-248
Includes indexes
内容説明・目次
内容説明
Schubert varieties provide an inductive tool for studying flag varieties. 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 on the other.
目次
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.
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