• 1 Fields Institute for Research In Mathematical Sciences
• 2 Department of Mathematics and Statistics [Toronto]
• 3 Oyama National College of Technology
• 4 Department of Mathematics [Sapporo]

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 Loehr giving the expansion of $\widetilde{H}_{\lambda} (X;q,t)$ on the monomial basis.