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

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.

28 pages

References in corpus (1)

• Wreath Product Symmetric Functions

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