A Bijective Proof of a Factorization Formula for Specialized Macdonald Polynomials

摘要

Let μ and ν = (ν_1,...,ν_k) be partitions such that μ is obtained from ν by adding m parts of size r. Descouens and Morita proved algebraically that the modified Macdonald polynomials H_μ(X,q,t) satisfy the identity H_μ=H_νH_((rm)) when the parameter t is specialize to an mth root of unity. Descouens, Morita, and Numata proved this formula bijectively when r ≤ ν_k and r ∈ {1,2}. This note gives a bijective proof of the formula for all r ≤ ν_k.