| 书目名称 | Macdonald Polynomials | | 副标题 | Commuting Family of | | 编辑 | Masatoshi Noumi | | 视频video | | | 概述 | Provides an introduction to Macdonald polynomials requiring only an undergraduate knowledge of algebra and analysis.Presents selected topics that are easily accessible to readers with a background in | | 丛书名称 | SpringerBriefs in Mathematical Physics | | 图书封面 |  | | 描述 | This book is a volume of the Springer Briefs in Mathematical Physics and serves as an introductory textbook on the theory of Macdonald polynomials. It is based on a series of online lectures given by the author at the Royal Institute of Technology (KTH), Stockholm, in February and March 2021.. .Macdonald polynomials are a class of symmetric orthogonal polynomials in many variables. They include important classes of special functions such as Schur functions and Hall–Littlewood polynomials and play important roles in various fields of mathematics and mathematical physics. After an overview of Schur functions, the author introduces Macdonald polynomials (of type A, in the .GL.n. version) as eigenfunctions of a .q.-difference operator, called the Macdonald–Ruijsenaars operator, in the ring of symmetric polynomials. Starting from this definition, various remarkable properties of Macdonald polynomials are explained, such as orthogonality, evaluation formulas, and self-duality, with emphasis on the roles of commuting .q.-difference operators. The author also explains how Macdonald polynomials are formulated in the framework of affine Hecke algebras and .q.-Dunkl operators.. | | 出版日期 | Book 2023 | | 关键词 | symmetric functions; q-difference equation; q-orthogonal polynomial; quantum integrable system; Macdonal | | 版次 | 1 | | doi | https://doi.org/10.1007/978-981-99-4587-0 | | isbn_softcover | 978-981-99-4586-3 | | isbn_ebook | 978-981-99-4587-0Series ISSN 2197-1757 Series E-ISSN 2197-1765 | | issn_series | 2197-1757 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapor |
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发表于 2025-3-21 17:45:16
