The Grassmannian Variety

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Focusing on Grassmannian varieties and their Schubert subvarieties, this book explores their geometric and representation-theoretic dimensions. It serves as a valuable resource for graduate students and researchers in mathematics, physics, and computer science, bridging commutative algebra, algebraic geometry, representation theory, and combinatorics. Key topics include standard monomial theory (SMT) and its applications, such as the Cohen-Macaulay property, normality, Gorenstein property, and connections to classical invariant theory, enriching the understanding of algebraic geometry.