Research output: Contribution to journal › Article

**Boundary quantum Knizhnik-Zamolodchikov equations and fusion.** / Reshetikhin, Nicolai; Stokman, Jasper; Vlaar, Bart Hendrik Maarten.

Research output: Contribution to journal › Article

Reshetikhin, N, Stokman, J & Vlaar, BHM 2016, 'Boundary quantum Knizhnik-Zamolodchikov equations and fusion', *Annales Henri Poincare*, vol. 17, no. 1, pp. 137–177. https://doi.org/10.1007/s00023-014-0395-4

Reshetikhin, N., Stokman, J., & Vlaar, B. H. M. (2016). Boundary quantum Knizhnik-Zamolodchikov equations and fusion. *Annales Henri Poincare*, *17*(1), 137–177. https://doi.org/10.1007/s00023-014-0395-4

Reshetikhin N, Stokman J, Vlaar BHM. Boundary quantum Knizhnik-Zamolodchikov equations and fusion. Annales Henri Poincare. 2016 Jan;17(1):137–177. https://doi.org/10.1007/s00023-014-0395-4

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title = "Boundary quantum Knizhnik-Zamolodchikov equations and fusion",

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.",

keywords = "math.QA, math-ph, math.MP",

author = "Nicolai Reshetikhin and Jasper Stokman and Vlaar, {Bart Hendrik Maarten}",

note = "{\circledC} 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",

year = "2016",

month = "1",

doi = "10.1007/s00023-014-0395-4",

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pages = "137–177",

journal = "Annales Henri Poincare",

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AU - Stokman, Jasper

AU - Vlaar, Bart Hendrik Maarten

N1 - © 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

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N2 - 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.

AB - 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.

KW - math.QA

KW - math-ph

KW - math.MP

U2 - 10.1007/s00023-014-0395-4

DO - 10.1007/s00023-014-0395-4

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JO - Annales Henri Poincare

JF - Annales Henri Poincare

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