Abstract
We prove a strong factorization property of interpolation Macdonald polynomials when tends to . As a consequence, we show that Macdonald polynomials have a strong factorization property when tends to , which was posed as an open question in our previous paper with Féray. Furthermore, we introduce multivariate -Kostka numbers and we show that they are polynomials in with integer coefficients by using the strong factorization property of Macdonald polynomials. We conjecture that multivariate -Kostka numbers are in fact polynomials in with nonnegative integer coefficients, which generalizes the celebrated Macdonald s positivity conjecture.
Publication
J. Algebraic Combin., 46 (1), 135-163, 2017