ON THE POLYNOMIAL TAU-FUNCTIONS FOR THE KP HIERARCHY AND THE BISPECTRAL PROPERTY

We show that the tau-functions obtained from Schur polynomials lead to wave functions w(x1,x2,...;k) that possess the following bispectral property: There exists a differential operator B(k, partial derivative(k)), independent of x1, such that B(k, partial derivative(k))w = THETA(x1)w, where THETA(x1) is independent of k. This extends for the KP hierarchy some earlier results of J. J. Duistermaat and F. A. Grunbaum for the rational solutions of KdV and of P. Wright for certain rational solutions of the generalized KdV equations.