2003/10/18 by Boris Feigin, B. Feigin, Feigin, B. +12
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT
paper · pdf · doi:10.48550/arxiv.math/0310284
33 pages
arxiv created 2003/10/18 · openalex publication_date 2003/10/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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\bmod 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\bmod 2,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.