A Quantum Deformation of the Virasoro Algebra and the Macdonald Symmetric Functions

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.

15 pages, latex file

References in corpus (1)

• Collective fields, Calogero-Sutherland model and generalized matrix models

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