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Xiaoping Xu
Representations of Lie Algebras and Partial Differential Equations
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2397862Representations of Lie Algebras and Partial Differential Equationshttps://www.gandhi.com.mx/representations-of-lie-algebras-and-partial-differential-equations-9789811063916/phttps://gandhi.vtexassets.com/arquivos/ids/3032466/8843ef30-5cb0-4387-8787-677cc807abe8.jpg?v=63838478688300000026952994MXNSpringer Nature SingaporeInStock/Ebooks/<p>This book provides explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic codes, combinatorics and algebraic varieties, summarizing the authors works and his joint works with his former students. Further, it presents various oscillator generalizations of the classical representation theorem on harmonic polynomials, and highlights new functors from the representation category of a simple Lie algebra to that of another simple Lie algebra.</p><p>Partial differential equations play a key role in solving certain representation problems. The weight matrices of the minimal and adjoint representations over the simple Lie algebras of types E and F are proved to generate ternary orthogonal linear codes with large minimal distances. New multi-variable hypergeometric functions related to the root systems of simple Lie algebras are introduced in connection with quantum many-body systems in one dimension. In addition, the book identifies certain equivalent combinatorial properties on representation formulas, and the irreducibility of representations is proved directly related to algebraic varieties. The book offers a valuable reference guide for mathematicians and scientists alike. As it is largely self-contained readers need only a minimal background in calculus and linear algebra it can also be used as a textbook.</p>...2333857Representations of Lie Algebras and Partial Differential Equations26952994https://www.gandhi.com.mx/representations-of-lie-algebras-and-partial-differential-equations-9789811063916/phttps://gandhi.vtexassets.com/arquivos/ids/3032466/8843ef30-5cb0-4387-8787-677cc807abe8.jpg?v=638384786883000000InStockMXN99999DIEbook20179789811063916_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_<p>This book provides explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic codes, combinatorics and algebraic varieties, summarizing the authors works and his joint works with his former students. Further, it presents various oscillator generalizations of the classical representation theorem on harmonic polynomials, and highlights new functors from the representation category of a simple Lie algebra to that of another simple Lie algebra.</p><p>Partial differential equations play a key role in solving certain representation problems. The weight matrices of the minimal and adjoint representations over the simple Lie algebras of types E and F are proved to generate ternary orthogonal linear codes with large minimal distances. New multi-variable hypergeometric functions related to the root systems of simple Lie algebras are introduced in connection with quantum many-body systems in one dimension. In addition, the book identifies certain equivalent combinatorial properties on representation formulas, and the irreducibility of representations is proved directly related to algebraic varieties. The book offers a valuable reference guide for mathematicians and scientists alike. As it is largely self-contained readers need only a minimal background in calculus and linear algebra it can also be used as a textbook.</p>9789811063916_Springer Singaporelibro_electonico_eb6cd6d0-0eaf-3bd9-976d-73d2856a5917_9789811063916;9789811063916_9789811063916Xiaoping XuInglésMéxicoSpringer Nature Singapore2017-10-16T00:00:00+00:00