Letters in Mathematical Physics

, Volume 38, Issue 1, pp 33–51 | Cite as

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

  • Jun'Ichi Shiraishi
  • Harunobu Kubo
  • Hidetoshi Awata
  • Satoru Odake


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 


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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Jun'Ichi Shiraishi
    • 1
  • Harunobu Kubo
    • 2
  • Hidetoshi Awata
    • 3
  • Satoru Odake
    • 4
  1. 1.Institute for Solid State PhysicsUniversity of TokyoTokyoJapan
  2. 2.Department of Physics, Faculty of ScienceUniversity of TokyoTokyoJapan
  3. 3.Uji Research Center, Yukawa Institute for Theoretical PhysicsKyoto UniversityUjiJapan
  4. 4.Department of Physics, Faculty of ScienceShinshu UniversityMatsumotoJapan

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