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arXiv · 1404.6076

Pfaffian and determinantal tau functions I

J. W. van de Leur·A. Yu. Orlov
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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.

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J. W. van de Leur, A. Yu. Orlov. 2014-04-24. Pfaffian and determinantal tau functions I. https://doi.org/10.1007/s11005-015-0786-6

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