Polynomial tau-functions of KP and KdV type hierarchies

Johan van de Leur (Universiteit Utrecht)

Tuesday 19th March, 2019 16:00-17:00 Maths 311B


Sato showed that all Schur functions are polynomial tau-functions of the 1-component KP hierarchy.  The expression of this function as a determinant of elementary Schur functions can easily be adapted to obtain any polynomial tau-function of this hierarchy. The proof of this fact uses the 1-component boson-fermion correspondence. This approach can be applied to the s-component KP hierarchy, using the s-component boson-fermion correspondence, finding thereby all its polynomial tau-functions. We also find all polynomial tau-functions for the reduction of the s-component KP hierarchy, associated to any partition with s parts. This is joined work with Victor Kac

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