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A quantum deformation of the Virasoro algebra and the Macdonald symmetric functions |
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| Authors: | Jun'Ichi Shiraishi Harunobu Kubo Hidetoshi Awata Satoru Odake |
| Institution: | (1) Institute for Solid State Physics, University of Tokyo, 106 Tokyo, Japan;(2) Department of Physics, Faculty of Science, University of Tokyo, 113 Tokyo, Japan;(3) Uji Research Center, Yukawa Institute for Theoretical Physics, Kyoto University, 611 Uji, Japan;(4) Department of Physics, Faculty of Science, Shinshu University, 390 Matsumoto, Japan |
| 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. |
| Keywords: | 17B37 17B65 81R50 |
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