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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156972We 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.CombinatoricsA bijective proof of a factorization formula for Macdonald polynomials at roots of unitytext