Titlebook: Macdonald Polynomials; Commuting Family of Masatoshi Noumi Book 2023 The Editor(s) (if applicable) and The Author(s), under exclusive lice

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,Self-duality, Pieri Formula and?Cauchy Formulas,s chapter, we explain how the Pieri formulas (multiplication formula by .) are obtained from the action of Macdonald–Ruijsenaars operators . through the self-duality. We also investigate the Cauchy formula and the dual Cauchy formula for Macdonald polynomials and the relevant kernel identities.

外星人

,Affine Hecke Algebra and?,-Dunkl Operators (Overview),e .. (For a more comprehensive exposition, see Macdonald [22].) We explain how the commuting family of Macdonald–Ruijsenaars operators arise naturally in the framework of affine Hecke algebras. We also show how the self-duality of Macdonald polynomials can be established by means of the Cherednik involution of the double affine Hecke algebra.

干涉

2197-1757 that are easily accessible to readers with a background in 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 Tec

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,Littlewood–Richardson Coefficients and?Branching Coefficients, types of coefficients are intimately related to each other through the Cauchy formula for Macdonald polynomials. We also present a commuting family of .-difference operators of row type for which Macdonald polynomials are joint eigenfunctions, and explain how they are related to the Pieri formula of row type.

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Book 2023 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

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Book 2023ynomials 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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arrhythmic

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Schur Functions,e Schur functions, one by combinatorics of semi-standard tableaux, and the other in terms of ratios of Vandermonde-type determinants. Then we establish the equivalence of the two definitions by means of the Cauchy formula. It should be noted that the theory of Macdonald polynomials is modeled in man

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