Document Type

Article

Publication Date

12-2012

Abstract

Let μ and ν = (ν 1, . . . , ν k ) be partitions such that μ is obtained from ν by adding m parts of sizer. 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 .

Comments

This is the pre-published manuscript.

The version of record is available from the publisher at http://link.springer.com/article/10.1007%2Fs00026-012-0162-5.

Copyright © Springer Basel 2012. All rights reserved.

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