  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.
