Strong factorization property of Macdonald polynomials and higher-order Macdonald's positivity conjecture

Abstract

We prove a strong factorization property of interpolation Macdonald polynomials when q tends to 1. As a consequence, we show that Macdonald polynomials have a strong factorization property when q tends to 1, which was posed as an open question in our previous paper with Féray. Furthermore, we introduce multivariate q,t-Kostka numbers and we show that they are polynomials in q,t with integer coefficients by using the strong factorization property of Macdonald polynomials. We conjecture that multivariate q,t-Kostka numbers are in fact polynomials in q,t with nonnegative integer coefficients, which generalizes the celebrated Macdonald s positivity conjecture.

Publication
J. Algebraic Combin., 46 (1), 135-163, 2017