On the Expansion Coefficients of Tau-function of the BKP Hierarchy

Abstract

We study the series expansion of the tau function of the BKP hierarchy applying the addition formulae of the BKP hierarchy. Any formal power series can be expanded in terms of Schur functions. It is known that, under the condition $\tau (x)\ne 0$, a formal power series $\tau (x)$ is a solution of the KP hierarchy if and only if its coefficients of Schur function expansion are given by the so called Giambelli type formula. A similar result is known for the BKP hierarchy with respect to Schur's Q-function expansion under a similar condition. In this paper we generalize this result to the case of $\tau (0)=0$.

arXiv comment18pages

References in corpus (6)

• T-systems and Y-systems in integrable systems
• Classical tau-function for quantum spin chains
• Schur function expansions of KP tau functions associated to algebraic curves
• On Addition Formulae of KP, mKP and BKP Hierarchies
• Hypergeometric functions related to Schur Q-polynomials and BKP equation
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Cited by in corpus (3)

• Isotropic Grassmannians, Plücker and Cartan maps
• Extended Schur's $Q$-functions and the full Kostant--Toda hierarchy on the Lie algebra of type $D$
• Drinfeld-Sokolov Hierarchies, Tau Functions, and Generalized Schur Polynomials