Standard Monomial Theory

• 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.

From the reviews: "The goal of the book is to present the results of Classical Invariant Theory (CIT) and Standard Monomial Theory (SMT) and the connection between the two theories. ... The book is written for a broad audience including prospective graduate students and young researchers. The exposition is self-contained. It may be used for a year long course on Invariant Theory and Schubert varieties." (Dmitrii A. Timashev, Mathematical Reviews, Issue 2008 m) "The book aims to describe the beautiful connection between Schubert varieties and their Standard Monomial Theory (SMT) on the one hand and Classical Invariant Theory (CIT) on the other. ... make the presentation self-contained keeping in mind the needs of prospective graduate students and young researchers. ... The book may be recommended as a nice introduction to SMT and related active research areas. It may be used for a year long course on Invariant Theory and Schubert varieties." (Ivan V. Arzhantsev, Zentralblatt MATH, Vol. 1137 (15), 2008)