Affine Hecke algebras and raising operators for Macdonald polynomials

Details Affine Hecke algebras and raising operators for Macdonald polynomials Affine Hecke algebras and raising operators for Macdonald polynomials

1996-05-04

arxiv.org/abs/q-alg/9605004v1

Mathematics

Quantum Algebra

35 pages, AMSTEX

Scientific paper

We introduce certain raising and lowering operators for Macdonald polynomials (of type $A_{n-1}$) by means of Dunkl operators. The raising operators we discuss are a natural $q$-analogue of raising operators for Jack polynomials introduced by L.Lapointe and L.Vinet. As an application we prove the integrality of double Kostka coefficients. Double analog of the multinomial coefficients are introduced.

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