Boundary matrices for the higher spin six vertex model

Mangazeev, Vladimir V. (Department of Theoretical Physics, Research School of Physics and Engineering, Australian National University, Canberra, ACT 2601, Australia) ; Lu, Xilin (Department of Theoretical Physics, Research School of Physics and Engineering, Australian National University, Canberra, ACT 2601, Australia)

19 June 2019

Abstract: In this paper we consider solutions to the reflection equation related to the higher spin stochastic six vertex model. The corresponding higher spin R -matrix is associated with the affine quantum algebra Uq(sl(2)ˆ) . The explicit formulas for boundary K -matrices for spins s=1/2,1 are well known. We derive difference equations for the generating function of matrix elements of the K -matrix for any spin s and solve them in terms of hypergeometric functions. As a result we derive the explicit formula for matrix elements of the K -matrix for arbitrary spin. In the lower- and upper- triangular cases, the K -matrix simplifies and reduces to simple products of q -Pochhammer symbols.


Published in: Nuclear Physics B 945 (2019) DOI: 10.1016/j.nuclphysb.2019.114665
License: CC-BY-3.0



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