Affine Hecke algebras and raising operators for Macdonald polynomials
classification
q-alg
math.QA
keywords
operatorsraisingpolynomialscoefficientsdoubleintroducedmacdonaldaffine
read the original abstract
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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Non-commutative creation operators for symmetric polynomials
Non-commutative creation operators B̂_m are built for symmetric polynomials in matrix and Fock representations of W_{1+∞} and affine Yangian algebras.
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