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arXiv · 2210.13862

On a conjecture on 2-reduced Schur functions and Schur's Q-functions

Yuta Nishiyama
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Abstract

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.

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Yuta Nishiyama. 2022-10-25. On a conjecture on 2-reduced Schur functions and Schur's Q-functions. https://arxiv.org/abs/2210.13862

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