论文标题
关于2还原的Schur功能和Schur的Q-功能的猜想
On a conjecture on 2-reduced Schur functions and Schur's Q-functions
论文作者
论文摘要
由Sato和Mori在Korteweg-de Vries（KDV）方程以及修改后的KDV方程，Mizukawa，Nakajima和Yamada的工作的动机中提出了猜想，并对2降低的Schur功能和Schur的Q-Finctions提出了猜测。猜想声称，Littlewood-Richardson系数的某些产品和两个2还原的Schur功能等于Schur的Q-功能，直至标量倍数。在本文中，我们给出了尚未证明的猜想的证明。我们介绍了Schur Q-功能的新表达，并使用它来证明猜想。还使用了逆Kostka矩阵的组合学。在通常的情况下，我们还考虑了猜想。
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.
