$q$-Difference raising operators for Macdonald polynomials and the integrality of transition coefficients

Details $q$-Difference raising operators for Macdonald polynomials and the integrality of transition coefficients $q$-Difference raising operators for Macdonald polynomials and the integrality of transition coefficients

1996-05-04

arxiv.org/abs/q-alg/9605005v1

Mathematics

Quantum Algebra

20 pages, AMSTEX

Scientific paper

We study certain $q$-difference raising operators for Macdonald polynomials (of type $A_{n-1}$) which are originated from the $q$-difference-reflection operators introduced in our previous paper. These operators can be regarded as a $q$-difference version of the raising operators for Jack polynomials introduced by L.Lapointe and L.Vinet. As an application of our $q$-difference raising operators we give an elementary proof of the integrality of the double Kostka coefficients which had been conjectured I.G. Macdonald. We also determine their quasi-classical limits, which give rise to (differental) raising operators for Jack polynomials.

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