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arXiv 2005.026652020-05math.RThep-thmath-phmath.MP

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

Victor G. Kac, Natasha Rozhkovskaya, Johan van de Leur

备注：: 28 pages
DOI：: 10.1063/5.0013017

英文摘要：

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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