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

@inproceedings{Descouens2008ABP,
  title={A bijective proof of a factorization formula for Macdonald polynomials at roots of unity},
  author={François Descouens and Hideaki Morita and Yasuhide Numata},
  year={2008}
}
We give a combinatorial proof of the factorization formula of modified Macdonald polynomials e Hλ(X; q, t) when t is specialized at a primitive root of unity. Our proof is restricted to the special case where λ is a two columns partition. We mainly use the combinatorial interpretation of Haiman, Haglund and Loehr giving the expansion of e Hλ(X; q, t) on the monomial basis. Résumé. Nous présentons une preuve combinatoire de la formule de factorisation des polynômes de Macdonald modifiés e Hλ(X… CONTINUE READING