  It is well-known that a BKP tau-function is the square root of a certain KP
tau-function, provided one puts the even KP times equal to zero. In this paper
we compute for all polynomial BKP tau-function its corresponding KP "square".
We also give, in the polynomial case, a representation theoretical proof of a
recent result by Alexandov, viz. that a KdV tau-function becomes a BKP
tau-function when one divides all KdV times by 2.
