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 Shiraishi
  • Harunobu Kubo
  • Hidetoshi Awata
  • Satoru Odake
Article

DOI: 10.1007/BF00398297

Cite this article as:
Shiraishi, J., Kubo, H., Awata, H. et al. Lett Math Phys (1996) 38: 33. doi:10.1007/BF00398297

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)

17B3717B6581R50

Key words

quantum deformationVirasoro algebrabosonic realizationMacdonald symmetric functions

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