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Local fields (Algebra) --- Representations of groups. --- Automorphic forms. --- Galois theory.

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This book gives a comprehensive treatment of the Grassmannian varieties and their Schubert subvarieties, focusing on the geometric and representation-theoretic aspects of Grassmannian varieties. Research of Grassmannian varieties is centered at the crossroads of commutative algebra, algebraic geometry, representation theory, and combinatorics. Therefore, this  text uniquely presents an exciting playing field  for graduate students and researchers in mathematics, physics, and computer science, to expand their knowledge in the field of algebraic geometry. The standard monomial theory (SMT) for the Grassmannian varieties and their Schubert subvarieties are introduced and the text presents some important applications of SMT including the Cohen–Macaulay property, normality, unique factoriality, Gorenstein property, singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory. This text would serve well as a reference book for a graduate work on Grassmannian varieties and would be an excellent supplementary text for several courses including those in geometry of spherical varieties, Schubert varieties, advanced topics in geometric and differential topology, representation theory of compact and reductive groups, Lie theory, toric varieties, geometric representation theory, and singularity theory. The reader should have some familiarity with commutative algebra and algebraic geometry.

Geometry --- Mathematics --- Physical Sciences & Mathematics --- Representations of groups. --- Geometry. --- Group representation (Mathematics) --- Groups, Representation theory of --- Mathematics. --- Algebraic geometry. --- Algebraic topology. --- Combinatorics. --- Algebraic Geometry. --- Algebraic Topology. --- Euclid's Elements --- Group theory --- Geometry, algebraic. --- Combinatorics --- Algebra --- Mathematical analysis --- Topology --- Algebraic geometry --- Combinatorics & graph theory. --- Math --- Science

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The volume is dedicated to Lev Sakhnovich, who made fundamental contributions in operator theory and related topics. Besides bibliographic material, it includes a number of selected papers related to Lev Sakhnovich's research interests. The papers are related to operator identities, moment problems, random matrices and linear stochastic systems.

Mathematics. --- Operator Theory. --- Systems Theory, Control. --- Probability Theory and Stochastic Processes. --- Operator theory. --- Systems theory. --- Distribution (Probability theory). --- Mathématiques --- Théorie des opérateurs --- Distribution (Théorie des probabilités) --- Distribution (Probability theory. --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Inverse scattering transform. --- Schur multiplier. --- Stochastic processes. --- Random processes --- Multiplier, Schur --- Scattering transform, Inverse --- Transform, Inverse scattering --- System theory. --- Probabilities. --- Probabilities --- Representations of groups --- Scattering (Mathematics) --- Transformations (Mathematics) --- Distribution functions --- Frequency distribution --- Characteristic functions --- Functional analysis --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Systems, Theory of --- Systems science --- Science --- Philosophy