  Motivated by Sato and Mori's work on the Korteweg-de Vries (KdV) equation and
the modified KdV equation, Mizukawa, Nakajima, and Yamada made a conjecture on
2-reduced Schur functions and Schur's Q-functions. The conjecture claims that
certain sums of products of a Littlewood-Richardson coefficient and two
2-reduced Schur functions are equal to Schur's Q-functions up to a scalar
multiple. In this paper we give a proof of the conjecture in cases which have
not been proved yet. We introduce a new expression of Schur's Q-functions and
use it to prove the conjecture. Combinatorics of the inverse Kostka matrix is
also used. We also provide consideration of the conjecture in general case.
