UNITARY QUANTUM GROUPS, QUANTUM PROJECTIVE SPACES AND Q-OSCILLATORS


ARIK M., CELIK S.

ZEITSCHRIFT FUR PHYSIK C-PARTICLES AND FIELDS, vol.59, no.1, pp.99-103, 1993 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 59 Issue: 1
  • Publication Date: 1993
  • Doi Number: 10.1007/bf01555843
  • Title of Journal : ZEITSCHRIFT FUR PHYSIK C-PARTICLES AND FIELDS
  • Page Numbers: pp.99-103

Abstract

We discuss the parametrization of quantum groups in terms of independent operators. We find that this consideration leads to the parametrization of SU(q)(2) in terms of a q-oscillator plus a commuting phase. The commuting phase is naturally identified with the subgroup U(1)and the remaining coset SU(q)(2)/U(1)=CP(q)(1) consists of a q-oscillator. For unitary quantum groups SU(q)(n), the analogous construction results in the quantum projective space SU(q)(n + 1)/U(q)(n)=CP(q)(n) being identified with the n-dimensional q-oscillator. This yields a nonlinear action of the quantum group SU(q)(n + 1) on the n-dimensional q-oscillator.