Article

Letters in Mathematical Physics

, Volume 38, Issue 1, pp 33-51

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

  • Jun'Ichi ShiraishiAffiliated withInstitute for Solid State Physics, University of Tokyo
  • , Harunobu KuboAffiliated withDepartment of Physics, Faculty of Science, University of Tokyo
  • , Hidetoshi AwataAffiliated withUji Research Center, Yukawa Institute for Theoretical Physics, Kyoto University
  • , Satoru OdakeAffiliated withDepartment of Physics, Faculty of Science, Shinshu University

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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.

Mathematics Subject Classifications (1991)

17B37 17B65 81R50

Key words

quantum deformation Virasoro algebra bosonic realization Macdonald symmetric functions