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}
}
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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