On an extension of the generalized BGW tau-function

Abstract

For an arbitrary solution to the Burgers–KdV hierarchy, we define the tau-tuple $$(\tau _1,\tau _2)$$ of the solution. We show that the product $$\tau _1\tau _2$$ admits Buryak’s residue formula. Therefore, according to Alexandrov’s theorem, $$\tau _1\tau _2$$ is a tau-function of the KP hierarchy. We then derive a formula for the affine coordinates for the point of the Sato Grassmannian corresponding to the tau-function $$\tau _1\tau _2$$ explicitly in terms of those for $$\tau _1$$ . Applications to the analogous open extension of the generalized BGW tau-function and to the open partition function are given.