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arXiv · 2005.02665

Polynomial Tau-functions of the KP, BKP, and the s-Component KP Hierarchies

Victor G. Kac·Natasha Rozhkovskaya·Johan van de Leur
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Abstract

We show that any polynomial tau-function of the s-component KP and the BKP hierarchies can be interpreted as a zero mode of an appropriate combinatorial generating function. As an application, we obtain explicit formulas for all polynomial tau-functions of these hierarchies in terms of Schur polynomials and Q-Schur polynomials respectively. We also obtain formulas for polynomial tau-functions of the reductions of the s-component KP hierarchy associated to partitions in s parts.

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Victor G. Kac, Natasha Rozhkovskaya, Johan van de Leur. 2020-05-06. Polynomial Tau-functions of the KP, BKP, and the s-Component KP Hierarchies. https://doi.org/10.1063/5.0013017

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