, Volume 38, Issue 1, pp 33-51

A quantum deformation of the Virasoro algebra and the Macdonald symmetric functions

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Abstract

A quantum deformation of the Virasoro algebra is defined. The Kac determinants at arbitrary levels are conjectured. We construct a bosonic realization of the quantum deformed Virasoro algebra. Singular vectors are expressed by the Macdonald symmetric functions. This is proved by constructing screening currents acting on the bosonic Fock space.