Geodesic
On a $c$-number quantum $\tau $-function
Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 1, pp. 119-131

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We first review the properties of the conventional $\tau$-functions of the KP and Toda-lattice hierarchies. A straightforward generalization is then discussed. It corresponds to passing from differential to finite-difference equations; it does not involve however the concept of operator-valued $\tau$-function nor the one associated with non-Cartanian (level $k\ne 1$) algebras. The present study could be useful to understand better $q$-free fields and their relation to ordinary free fields. 
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A. D. Mironov; A. Yu. Morozov; L. Vinet. On a $c$-number quantum $\tau $-function. Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 1, pp. 119-131. http://geodesic.mathdoc.fr/item/TMF_1994_100_1_a11/