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Macdonald polynomialscommuting family of q-difference operators and their joint Eigenfunctions /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Macdonald polynomialsby Masatoshi Noumi.
Reminder of title:	commuting family of q-difference operators and their joint Eigenfunctions /
Author:	Noumi, Masatoshi.
Published:	Singapore :Springer Nature Singapore :2023.
Description:	viii, 132 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Polynomials.
Online resource:	https://doi.org/10.1007/978-981-99-4587-0
ISBN:	9789819945870$q(electronic bk.)

Macdonald polynomialscommuting family of q-difference operators and their joint Eigenfunctions /
Noumi, Masatoshi.

Macdonald polynomialscommuting family of q-difference operators and their joint Eigenfunctions /[electronic resource] :by Masatoshi Noumi. - Singapore :Springer Nature Singapore :2023. - viii, 132 p. :ill., digital ;24 cm. - SpringerBriefs in mathematical physics,v. 502197-1765 ;. - SpringerBriefs in mathematical physics ;v.1..

Overview of Macdonald polynomials -- Preliminaries on symmetric functions -- Schur functions -- Macdonald polynomials: Definition and examples -- Orthogonality and higher order q-diﬀerence operators -- Self-duality, Pieri formula and Cauchy formulas -- Littlewood-Richardson coefficients and branching coefficients -- Affine Hecke algebra and q-Dunkl operators (overview)

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.

ISBN: 9789819945870$q(electronic bk.)

Standard No.: 10.1007/978-981-99-4587-0doiSubjects--Topical Terms:

184760
Polynomials.

LC Class. No.: QA161.P59

Dewey Class. No.: 515.55

Macdonald polynomialscommuting family of q-difference operators and their joint Eigenfunctions /
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520 $a 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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