Boundary quantum Knizhnik-Zamolodchikov equations and fusion

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Publication details

Journal Annales Henri Poincare E-pub ahead of print - 3 Jan 2015 Published (current) - Jan 2016 1 17 41 137–177 3/01/15 English

Abstract

In this paper we extend our previous results concerning Jackson integral solutions of the boundary quantum Knizhnik-Zamolodchikov equations with diagonal K-operators to higher-spin representations of quantum affine $\mathfrak{sl}_2$. First we give a systematic exposition of known results on $R$-operators acting in the tensor product of evaluation representations in Verma modules over quantum $\mathfrak{sl}_2$. We develop the corresponding fusion of $K$-operators, which we use to construct diagonal $K$-operators in these representations. We construct Jackson integral solutions of the associated boundary quantum Knizhnik-Zamolodchikov equations and explain how in the finite-dimensional case they can be obtained from our previous results by the fusion procedure.

Bibliographical note

© 2016 Springer International Publishing AG. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details
36 pages; some small additions and corrections concerning mero-uniform convergence (Defn. 6.1) and rectified some notation issues for the function \mathcal{Y} (p21 and onwards). appears in Annales Henri Poincar\'e, 2014

Research areas

• math.QA, math-ph, math.MP

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