| 书目名称 | Representations of Lie Algebras and Partial Differential Equations | | 编辑 | Xiaoping Xu | | 视频video | | | 概述 | Presents explicit representations of Lie algebras.Addresses interactions with partial differential equations.Examines associated new hypergeometric functions with root systems and quantum many-body sy | | 图书封面 |  | | 描述 | .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 author’s 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..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 v | | 出版日期 | Book 2017 | | 关键词 | Representations of Lie Algebras; Special Linear Algebras; Even Orthogonal Lie Algebras; Odd Orthogonal | | 版次 | 1 | | doi | https://doi.org/10.1007/978-981-10-6391-6 | | isbn_softcover | 978-981-13-4869-3 | | isbn_ebook | 978-981-10-6391-6 | | copyright | Springer Nature Singapore Pte Ltd. 2017 |
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发表于 2025-3-21 16:28:34
