On a c-number quantum $\tau$-function

Abstract

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.

12 pages, ITEP M-8/93, FIAN/TD-22/93, CRM-1934 (minor changes)

References in corpus (2)

• $q$--Hypergeometric Functions in the Formalism of Free Fields
• Integrable structures in matrix models and physics of 2d-gravity

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