TY - JOUR
T1 - A functional model for the tensor product of level 1 highest and level-1 lowest modules for the quantum affine algebra Uq(sl2)
AU - Feigin, B.
AU - Jimbo, M.
AU - Kashiwara, Masaki
AU - Miwa, Tetsuji
AU - Mukhin, E.
AU - Takeyama, Y.
PY - 2004/11
Y1 - 2004/11
N2 - 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(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-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.
AB - 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(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-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.
UR - http://www.scopus.com/inward/record.url?scp=4444339714&partnerID=8YFLogxK
U2 - 10.1016/j.ejc.2003.11.005
DO - 10.1016/j.ejc.2003.11.005
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AN - SCOPUS:4444339714
SN - 0195-6698
VL - 25
SP - 1197
EP - 1229
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
IS - 8
ER -