Martha Yip

University of Wisconsin, Madison

A Littlewood-Richardson rule for Macdonald polynomials

Symmetric Macdonald polynomials are multivariate polynomials with two
parameters q and t that are associated to root systems. For special
values of q and t, they specialize to well-known symmetric functions
such as Schur polynomials.

Using alcove walks as a combinatorial model, we give a formula for the
product of symmetric Macdonald polynomials in terms of the Macdonald
basis.