Pfaffian and determinantal tau functions I

Abstract

Adler, Shiota and van Moerbeke observed that a tau function of the Pfaff lattice is a square root of a tau function of the Toda lattice hierarchy of Ueno and Takasaki. In this paper we give a representation theoretical explanation for this phenomenon. We consider 2-BKP and two-component 2-KP tau functions. We shall show that a square of a BKP tau function is equal to a certain two-component KP tau function and a square of a 2-BKP tau function is equal to a certain two-component 2-KP tau function.

References in corpus (1)

• Random Bures mixed states and the distribution of their purity

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• Matrix model for the total descendant potential of a simple singularity of type $D$
• Rank shift conditions and reductions of 2d-Toda theory