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.
| Original language | English |
|---|---|
| Pages (from-to) | 137–177 |
| Number of pages | 41 |
| Journal | Annales Henri Poincare |
| Volume | 17 |
| Issue number | 1 |
| Early online date | 3 Jan 2015 |
| DOIs | |
| Publication status | Published - Jan 2016 |
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 details36 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
Keywords
- math.QA
- math-ph
- math.MP