Affine Hecke algebras and raising operators for Macdonald polynomials
Anatol N. Kirillov, Masatoshi Noumi
Abstract
We introduce certain raising and lowering operators for Macdonald polynomials (of type An-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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