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arXiv · 0803.2311

A bijective proof of a factorization formula for Macdonald polynomials at roots of unity

Francois Descouens·Hideaki Morita·Yasuhide Numata
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Abstract

We give a combinatorial proof of the factorization formula of modified Macdonald polynomials when the parameter t is specialized at a primitive root of unity. Our proof is restricted to the special case of partitions with 2 columns. We mainly use the combinatorial interpretation of Haglund, Haiman and Loehr giving the expansion of the modified Macdonald polynomials on the monomial basis.

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Francois Descouens, Hideaki Morita, Yasuhide Numata. 2008-03-15. A bijective proof of a factorization formula for Macdonald polynomials at roots of unity. https://arxiv.org/abs/0803.2311

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