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

Jun'ichi Shiraishi·Harunobu Kubo·Hidetoshi Awata·Satoru Odake
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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.

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Jun'ichi Shiraishi, Harunobu Kubo, Hidetoshi Awata, Satoru Odake. 1995-08-06. A Quantum Deformation of the Virasoro Algebra and the Macdonald Symmetric Functions. https://doi.org/10.1007/bf00398297

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