Standard Monomial Theory Invariant Theoretic Approach /

• Main Authors: Lakshmibai, Venkatramani (Author), Raghavan, Komaranapuram N. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.
• Series: Encyclopaedia of Mathematical Sciences, 137
• Subjects: Mathematics.; Algebra.; Algebraic geometry.; Algebraic Geometry.

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 o...

Table of Contents:

• 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.