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Macdonald polynomials : commuting family of q-difference operators and their joint Eigenfunctions / Masatoshi Noumi.

9789819945870 (electronic bk.)
9819945879 (electronic bk.)
9789819945863
9819945860

Singapore : Springer, 2023.

English

1 online resource (viii, 132 pages) : illustrations.

10.1007/978-981-99-4587-0 doi

QA161.P59

515/.55

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 GLn 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.

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Online resource; title from PDF title page (SpringerLink, viewed September 18, 2023).

SpringerBriefs in mathematical physics ; v. 50. 2197-1765

Print version: 9789819945863

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