Abstract
We present a representation of the generalized p-Onsager algebras Op(An−1(1)), Op(Dn+1(2)), Op(Bn(1)), Op(B˜n(1)) and Op(Dn(1)) 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.
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