2015/03/27 by Yoko Shigyo, Shigyo, Yoko
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.1503.07977
openalex publication_date 2015/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study Giambelli type formula in the KP and the BKP hierarchies. Any formal power series τ(x) can be expanded by the Schur functions. It is known that τ(x) with τ(0)=1 is a solution of the KP hierarchy if and only if the coefficients of this expansion satisfy Giambelli type formula. It is proved by using Sato's theory of the KP hierarchy. Here we give an alternative proof based on the previously established results on the equivalence of the addition formulae and the KP hierarchy without using Sato's theory. This method of the proof can also be applied to the case of the BKP hierarchy.