Bosonic realizations of higher-level toroidal Lie algebras

Naihuan Jing, Kailash Misra and Shaobin Tan

Vol. 219 (2005), No. 2, 285–301

DOI: 10.2140/pjm.2005.219.285

Abstract

We construct realizations for the 2-toroidal Lie algebra associated with the Lie algebra A₁ using vertex operators based on bosonic fields. In particular our construction realizes higher-level representations of the 2-toroidal algebra for any given pair of levels (k₀,k₁) with k₀≠0. We also construct a smaller module of level (k₀,0) for the toroidal algebra from the Fock space using certain screening vertex operator, and this later representation generalizes the higher-level construction of the affine Lie algebra sl₂.

Keywords

toroidal Lie algebra, vertex operator, bosonic realization

Mathematical Subject Classification 2000

Primary: 17B65, 17B69

Milestones

Received: 2 October 2002

Revised: 18 March 2004

Published: 1 April 2005