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The representation theory of symmetric groups is one of the most beautiful, popular and important parts of algebra, with many deep relations to other areas of mathematics such as combinatories, Lie theory and algebraic geometry. Kleshchev describes a new approach to the subject, based on the recent work of Lascoux, Leclerc, Thibon, Ariki, Grojnowski and Brundan, as well as his own. Much of this work has previously appeared only in the research literature. However to make it accessible to graduate students, the theory is developed from scratch, the only prerequisite being a standard course in abstract algebra. For the sake of transparency, Kleshchev concentrates on symmetric and spin-symmetric groups, though methods he develops are quite general and apply to a number of related objects. In sum, this unique book will be welcomed by graduate students and researchers as a modern account of the subject.

Linear algebraic groups. --- Representations of groups. --- Algebras, Linear. --- Geometry, Projective. --- Symmetry groups. --- Groups, Symmetry --- Symmetric groups --- Crystallography, Mathematical --- Quantum theory --- Representations of groups --- Projective geometry --- Geometry, Modern --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Algebraic groups, Linear --- Geometry, Algebraic --- Algebraic varieties --- Modular representations of groups. --- Hecke algebras. --- Superalgebras. --- Nonassociative algebras --- Algebras, Hecke --- Group algebras

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This book presents the main results of extensive research on the diffraction, radiation and propagation of elastic waves in isotropic and anisotropic media and bodies of various shapes based on integral equations, the separation of variables, the method of Green's functions, the method of finite elements, and the method of boundary elements. It explores the application of methods and equations of the theory of diffraction to the problems of synthesis of hydroacoustic antennas, and considers the spatial characteristics of loudspeakers. The book also provides a detailed description of the acoustic monitoring of oil products in different volumes.

Elastic waves.