A bijective proof of a factorization formula for Macdonald polynomials at roots of unity
A bijective proof of a factorization formula for Macdonald polynomials at roots of unity
We give a combinatorial proof of the factorization formula of modified Macdonald polynomials $\widetilde{H}_{\lambda} (X;q,t)$ when $t$ is specialized at a primitive root of unity. Our proof is restricted to the special case where $\lambda$ is a two columns partition. We mainly use the combinatorial interpretation of Haiman, Haglund and …