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On connection matrices of quantum Knizhnik-Zamolodchikov equations based on Lie super algebras

2015/10/14 by W. Galleas, Galleas, W., J. V. Stokman +1
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #math-ph #math.MP #math.QA #nlin.SI

paper · pdf · doi:10.48550/arxiv.1510.04318

27 pages; v2: typos fixed and references added; v3: small corrections; v4: version accepted for publication in Adv. Stud. Pure Math

arxiv created 2016/07/15 · arxiv updated 2016/07/18

Abstract

We propose a new method to compute connection matrices of quantum Knizhnik-Zamolodchikov equations associated to integrable vertex models with super algebra and Hecke algebra symmetries. The scheme relies on decomposing the underlying spin representation of the affine Hecke algebra in principal series modules and invoking the known solution of the connection problem for quantum affine Knizhnik-Zamolodchikov equations associated to principal series modules. We apply the method to the spin representation underlying the Uq(\mathfrakgl(2|1)) Perk-Schultz model. We show that the corresponding connection matrices are described by an elliptic solution of a supersymmetric version of the dynamical quantum Yang-Baxter equation with spectral parameter.

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