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Boundary quantum Knizhnik-Zamolodchikov equations and fusion

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

In: Annales Henri Poincare, Vol. 17, No. 1, 01.2016, p. 137–177.

Research output: Contribution to journalArticle

Harvard

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

APA

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

Vancouver

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

Author

Reshetikhin, Nicolai ; Stokman, Jasper ; Vlaar, Bart Hendrik Maarten. / Boundary quantum Knizhnik-Zamolodchikov equations and fusion. In: Annales Henri Poincare. 2016 ; Vol. 17, No. 1. pp. 137–177.

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@article{f939a6a2acbb4387b238a383595835f6,
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",
language = "English",
volume = "17",
pages = "137–177",
journal = "Annales Henri Poincare",
issn = "1424-0661",
publisher = "Birkhauser Verlag Basel",
number = "1",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Boundary quantum Knizhnik-Zamolodchikov equations and fusion

AU - Reshetikhin, Nicolai

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

PY - 2016/1

Y1 - 2016/1

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

M3 - Article

VL - 17

SP - 137

EP - 177

JO - Annales Henri Poincare

JF - Annales Henri Poincare

SN - 1424-0661

IS - 1

ER -