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The Brezin-Gross-Witten (BGW) model is one of the basic examples in the classof non-eigenvalue unitary matrix models. The generalized BGW tau-function$\tau_N$ was constructed from a one parametric deformation of the original BGWmodel using the generalized Kontsevich model representation. It is atau-function of the KdV hierarchy for any value of $N\in{\mathbb C}$, where thecase $N=0$ reduces to the original BGW tau-function. In this paper, we presenta representation of $\tau_N$ in terms of the $W_{1+\infty}$ operators thatpreserves the KP integrability. This naturally establishes a connection betweenthe (generalized) BGW and Kontsevich-Witten tau-functions using $GL(\infty)$operators, both considered as the basic building blocks in the theory of matrixmodels and partition functions.

A connection between the Kontsevich-Witten and Brezin-Gross-Witten tau-functions