A functional model for the tensor product of level 1 highest and level-1 lowest modules for the quantum affine algebra Uq(sl2)

B. Feigin*, M. Jimbo, Masaki Kashiwara, Tetsuji Miwa, E. Mukhin, Y. Takeyama

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Let V(Λi) (resp., V(-Λj)) be a fundamental integrable highest (resp., lowest) weight module of Uq(sl2). The tensor product V(Λi)⊗V(-Λj) is filtered by submodules Fn=Uq(sl2)(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(Λ10)). 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-jmod2,n-2l=m, whose members Pn,l=Pn,l (X1,...,Xl z1,...,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.

Original languageEnglish
Pages (from-to)1197-1229
Number of pages33
JournalEuropean Journal of Combinatorics
Volume25
Issue number8
DOIs
StatePublished - Nov 2004
Externally publishedYes

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