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

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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.
20 pages, AMSTEX

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Quantum Algebra

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http://salesiana.dossiersoluciones.com/handle/123456789/153532

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/q-alg/9605005
 http://arxiv.org/abs/q-alg/9605005

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arXiv