A functional model for the tensor product of level 1 highest and level -1 lowest modules for the quantum affine algebra Uq(sT2)

Let V(Λi) (resp., V(-Λj)) be a fundamental integrable highest (resp., lowest) weight module of Uq (sl^2). The tensor product V(Λi) ⊗ V(-Λj) is filtered by submodules Fn = Uq (sl^2)(vi ⊗ vn-i), n ≥ 0, n ≡ i-j mod 2, where vi ∈ V(Λi) is the highest vector and vn-i ∈ V(-Λj is an extremal vector. We show that Fn/Fn+2 is isomorphic to the level 0 extremal weight module V(n(Λ1 - Λ0)). Using this we give a functional realization of the completion of V(Λi) ⊗ V(-Λj) by the filtration (Fn)n≥0. The subspace of V(Λi) ⊗ V(-Λj) of sl2-weight m is mapped to a certain space of sequences (Pn,l)n≥0,n≡i-j mod 2, n-2l=m, whose members Pn,l = Pn,l (X1,...,Xl | zl,..., zn) are symmetric polynomials in Xa and symmetric Laurent polynomials in zk, with additional constraints. When the parameter q is specialized to √-1, this construction settles a conjecture which arose in the study of form factors in integrable field theory.

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