A summation formula for Macdonald polynomials
arXiv:1506.06597 · doi:10.1007/s11005-016-0820-3
Abstract
We derive an explicit sum formula for symmetric Macdonald polynomials. Our expression contains multiple sums over the symmetric group and uses the action of Hecke generators on the ring of polynomials. In the special cases and , we recover known expressions for the monomial symmetric and Hall-Littlewood polynomials, respectively. Other specializations of our formula give new expressions for the Jack and -Whittaker polynomials.
8 pages