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Article

Pfaffian and Determinantal Tau Functions

Letters in Mathematical Physics. 2015. Vol. 105. P. 1499--1531.
van de Leur J., Orlov A. Y.

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. © 2015 The Author(s)