Generalized $q$-deformation of Virasoro Algebra

Abstract

We find a extension of the q-deformed Virasoro algebra. This deformation includes on an equal footing the usual q-deformed oscillators and the ``quons" of infinite statistics. Various representations of Virasoro algebra, both differential and oscillator representation, are considered. A new relization of the generalized q-deformed centerless Virasoro algebra is constructed by introducing a so-called power raising operator.