Reflection $K$ matrices associated with an Onsager coideal of $U_p(A_{n-1}^{(1)})$, $U_p(B_n^{(1)})$, $U_p(D_n^{(1)})$ and $U_p(D_{n+1}^{(2)})$

Abstract

We determine the intertwiners of a family of Onsager coideal subalgebras of the quantum affine algebra $U_p(A_{n-1}^{(1)})$ in the fundamental representations and $U_p(B_n^{(1)}),U_p(D_n^{(1)}),U_p(D_{n+1}^{(2)})$ in the spin representations. They reproduce the reflection $K$ matrices obtained recently by the matrix product construction connected to the three dimensional integrability. In particular the present approach provides the first proof of the reflection equation for the non type $A$ cases.

arXiv comment20 pages, minor correction

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Cited by in corpus (2)

• Integrable boundaries for the q-Hahn process
• Tetrahedron and 3D reflection equation from PBW bases of the nilpotent subalgebra of quantum superalgebras