Pfaffian and determinantal tau functions I
Mathematical Physics
2015-09-02 v1 math.MP
Exactly Solvable and Integrable Systems
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.
Cite
@article{arxiv.1404.6076,
title = {Pfaffian and determinantal tau functions I},
author = {J. W. van de Leur and A. Yu. Orlov},
journal= {arXiv preprint arXiv:1404.6076},
year = {2015}
}