This article is a direct continuation of  where we begun the study of the transfer matrix spectral problem for the cyclic representations of the trigonometric 6-vertex reflection algebra associated to the Bazhanov-Stroganov Lax operator. There we addressed this problem for the case where one of the K-matrices describing the boundary conditions is triangular. In the present article we consider the most general integrable boundary conditions, namely the most general boundary K-matrices satisfying the reflection equation. The spectral analysis is developed by implementing the method of Separation of Variables (SoV). We first design a suitable gauge transformation that enable us to put into correspondence the spectral problem for the most general boundary conditions with another one having one boundary K-matrix in a triangular form. In these settings the SoV resolution can be obtained along an extension of the method described in . The transfer matrix spectrum is then completely characterized in terms of the set of solutions to a discrete system of polynomial equations in a given class of functions and equivalently as the set of solutions to an analogue of Baxter's T-Q functional equation. We further describe scalar product properties of the separate states including eigenstates of the transfer matrix.
Cited by 3
J M Maillet et al., On separation of variables for reflection algebras
J. Stat. Mech. 2019, 094020 (2019) [Crossref]
N Kitanine et al., The open XXZ spin chain in the SoV framework: scalar product of separate states
J. Phys. A: Math. Theor. 51, 485201 (2018) [Crossref]
Jean Michel Maillet et al., Complete spectrum of quantum integrable lattice models associated to Y(gl(n)) by separation of variables
SciPost Phys. 6, 071 (2019) [Crossref]