An Elliptic Algebra Uq,ₚ(sl₂) and the Fusion RSOS Model

الأصل · EN

We introduce an elliptic algebra Uq,ₚ(sl₂) with p=q²ʳ (r∈ >₀) 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 SU(2)ₖ× SU(2)ᵣ₋ₖ₋₂/SU(2)ᵣ₋₂. Extending the work by Lukyanov and Pugai corresponding to the case k=1, we gives a full set of screening operators for k>1. The algebra Uq,ₚ(sl₂) has two interesting degeneration limits, p→ 0 and p→ 1. The former limit yields the quantum affine algebra Uq(sl₂) whereas the latter yields the algebra Aℏ,η(sl₂), the scaling limit of the elliptic algebra Aq,ₚ(sl₂). 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.