Abstract
A factorization of modified Macdonald polynomials at roots of unity
Elizabeth Niese
Virginia Polytechnic Institute and State University
Macdonald polynomials have become central objects of study in the theory of symmetric functions. Descouens and Morita proved a factorization formula for the modified Macdonald polynomial when one parameter is set to a root of unity using symmetric function identities. They pose the problem of finding a bijective proof of this factorization using Haglund's combinatorial formula. In this talk I present a bijective proof of the factorization as well as a discussion of the univariate symmetry of the polynomials. This is joint work with Nicholas Loehr.
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