LEADER 03485nam 22005895 450 001 9910746083403321 005 20230908132825.0 010 $a981-9945-87-9 024 7 $a10.1007/978-981-99-4587-0 035 $a(MiAaPQ)EBC30736593 035 $a(Au-PeEL)EBL30736593 035 $a(DE-He213)978-981-99-4587-0 035 $a(PPN)272737208 035 $a(EXLCZ)9928172726200041 100 $a20230908d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMacdonald Polynomials$b[electronic resource] $eCommuting Family of q-Difference Operators and Their Joint Eigenfunctions /$fby Masatoshi Noumi 205 $a1st ed. 2023. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2023. 215 $a1 online resource (137 pages) 225 1 $aSpringerBriefs in Mathematical Physics,$x2197-1765 ;$v50 311 08$aPrint version: Noumi, Masatoshi Macdonald Polynomials Singapore : Springer,c2023 9789819945863 327 $aOverview of Macdonald polynomials -- Preliminaries on symmetric functions -- Schur functions -- Macdonald polynomials: Definition and examples -- Orthogonality and higher order q-di?erence operators -- Self-duality, Pieri formula and Cauchy formulas -- Littlewood?Richardson coefficients and branching coefficients -- Affine Hecke algebra and q-Dunkl operators (overview). 330 $aThis book is a volume of the Springer Briefs in Mathematical Physics and serves as an introductory textbook on the theory of Macdonald polynomials. It is based on a series of online lectures given by the author at the Royal Institute of Technology (KTH), Stockholm, in February and March 2021. Macdonald polynomials are a class of symmetric orthogonal polynomials in many variables. They include important classes of special functions such as Schur functions and Hall?Littlewood polynomials and play important roles in various fields of mathematics and mathematical physics. After an overview of Schur functions, the author introduces Macdonald polynomials (of type A, in the GLn version) as eigenfunctions of a q-difference operator, called the Macdonald?Ruijsenaars operator, in the ring of symmetric polynomials. Starting from this definition, various remarkable properties of Macdonald polynomials are explained, such as orthogonality, evaluation formulas, and self-duality, with emphasis on the roles of commuting q-difference operators. The author also explains how Macdonald polynomials are formulated in the framework of affine Hecke algebras and q-Dunkl operators. 410 0$aSpringerBriefs in Mathematical Physics,$x2197-1765 ;$v50 606 $aMathematical physics 606 $aSpecial functions 606 $aAssociative rings 606 $aAssociative algebras 606 $aMathematical Physics 606 $aSpecial Functions 606 $aAssociative Rings and Algebras 615 0$aMathematical physics. 615 0$aSpecial functions. 615 0$aAssociative rings. 615 0$aAssociative algebras. 615 14$aMathematical Physics. 615 24$aSpecial Functions. 615 24$aAssociative Rings and Algebras. 676 $a530.15 700 $aNoumi$b Masatoshi$0283693 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910746083403321 996 $aMacdonald Polynomials$93563070 997 $aUNINA