An Elliptic Algebra and the Fusion RSOS Model

Abstract:

We introduce an elliptic algebra with and present its free boson representation at generic level k. We show that this algebra governs a structure of the space of states in the k-fusion RSOS model specified by a pair of positive integers (r,k), or equivalently a q-deformation of the coset conformal field theory . Extending the work by Lukyanov and Pugai corresponding to the case k= 1, we give a full set of screening operators for k > 1. The algebra has two interesting degeneration limits, p→ 0 and p→ 1. The former limit yields the quantum affine algebra whereas the latter yields the algebra , the scaling limit of the elliptic algebra . Using this correspondence, we also obtain the highest component of two types of vertex operators which can be regarded as q-deformations of the primary fields in the coset conformal field theory.