New D_{n+1}^(2) K-matrices with quantum group symmetry

TL;DR

This paper introduces new solutions to the boundary Yang-Baxter equation for the $D_{n+1}^{(2)}$ model, revealing transfer matrices with specific quantum group symmetries and duality properties that explain spectral degeneracies.

Contribution

It presents novel families of K-matrices for the $D_{n+1}^{(2)}$ boundary Yang-Baxter equation with associated quantum group symmetries and duality features.

Findings

New K-matrices for $D_{n+1}^{(2)}$ boundary Yang-Baxter equation

Transfer matrices exhibit $U_q(B_{n-p}) imes U_q(B_p)$ symmetry

Duality symmetry explains spectral degeneracies

Abstract

We find new families of solutions of the $D_{n+1}^{(2)}$ boundary Yang-Baxter equation. The open spin-chain transfer matrices constructed with these K-matrices have quantum group symmetry corresponding to removing one node from the $D_{n+1}^{(2)}$ Dynkin diagram, namely, $U_{q}(B_{n-p}) \otimes U_{q}(B_{p})$, where $p=0, \ldots, n$. These transfer matrices also have a $p \leftrightarrow n-p$ duality symmetry. These symmetries help to account for the degeneracies in the spectrum of the transfer matrix.