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

```@article{Shiraishi1996AQD,
title={A quantum deformation of the Virasoro algebra and the Macdonald symmetric functions},
author={Jun'ichi Shiraishi and Harunobu Kubo and Hidetoshi Awata and Satoru Odake},
journal={Letters in Mathematical Physics},
year={1996},
volume={38},
pages={33-51}
}```
• Published 30 July 1995
• Mathematics
• Letters in Mathematical Physics
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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