MATRIX MODELS AT FINITE-N AND THE KP HIERARCHY

Abstract

We give an alternative proof that the partition function Z(n)(t(l)) of the hermitian one-matrix model at finite N is a particular Wronskian type tau-function of the KP hierarchy, and is related to the orthogonal polynomials P(n)(lambda, t) by P(n)(lambda, t) = lambda(n)Z(n)(t(l) + l-1-lambda(-l))/Z(n)(t(l)). We also derive a bilinear relation for the Baker-Akhiezer function of the matrix model, generalizing the bilinear identity of the KP hierarchy.