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[en] We present a representation of the generalized p-Onsager algebras , , , and in which the generators are expressed as local Hamiltonians of XXZ type spin chains with various boundary terms reflecting the Dynkin diagrams. Their symmetry is described by the reflection K matrices which are obtained recently by a q-boson matrix product construction related to the 3D integrability and characterized by Onsager coideals of quantum affine algebras. The spectral decomposition of the K matrices with respect to the classical part of the Onsager algebra is described conjecturally. We also include a proof of a certain invariance property of boundary vectors in the q-boson Fock space playing a key role in the matrix product construction.
[en] We construct a braiding operator in terms of the quantum dilogarithm function based on the quantum cluster algebra. We show that it is a q-deformation of the R-operator for which hyperbolic octahedron is assigned. Also shown is that, by taking q to be a root of unity, our braiding operator reduces to the Kashaev RK-matrix up to a simple gauge-transformation. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Cluster algebras in mathematical physics’. (paper)
[en] The effective theory for the hierarchical fractional quantum Hall (FQH) effect is proposed. We also derive the topological numbers K matrix and t vector and the general edge excitation from the effective theory. One can find that the two issues in rapidly rotating ultracold atoms are similar to those in electron FQH liquid.
[en] This work is concerned with the quasi-classical limit of the boundary quantum inverse scattering method for the twisted sl(2|1)(2) vertex model with diagonal K-matrices. In this limit Gaudin's Hamiltonians with diagonal boundary terms are presented and diagonalized
[en] The An-1 Gaudin model with integrable boundaries specified by non-diagonal K-matrices is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe ansatz method. The eigenvalues and the corresponding Bethe ansatz equations are obtained
[en] A self-consistent analysis of pion scattering and pion photoproduction within a coupled channels dynamical model is presented. In the case of pion photoproduction, we obtain background contributions to the imaginary part of the S-wave multipole which differ considerably from the result based on the K-matrix approximation. Within the dynamical model these background contributions become large and negative in the region of the S11(1535) resonance. Due to this fact much larger resonance contributions are required in order to explain the results of the recent multipole analyses. For the first S11(1535) resonance we obtain as a value of the dressed electromagnetic helicity amplitude: A1/2=(72±2)x10-3 GeV-1/2. Similar values can be derived from eta photoproduction if one takes the same total width (ΓR=95±5 MeV) as in pion scattering and pion photoproduction. The combined analysis yields considerable strength at invariant mass W≥1750 MeV, which can be explained by a third and a fourth S11 resonance with the masses 1846±47 and 2113±70 MeV