Duality and quantum-algebra symmetry of the A_{N-1}^(1) open spin chain with diagonal boundary fields

TL;DR

This paper demonstrates the symmetry properties of the A_{N-1}^(1) open spin chain with diagonal boundary fields, revealing duality and quantum algebra symmetries, and uses these to compute exact boundary S matrices.

Contribution

It uncovers the duality and quantum algebra symmetries of the open spin chain and applies these to derive exact boundary S matrices in the real q regime.

Findings

Identified U_q(SU(L)) x U_q(SU(N-L)) x U(1) symmetry

Discovered a duality symmetry exchanging L and N-L

Computed exact boundary S matrices for real q

Abstract

We show that the transfer matrix of the A_{N-1}^(1) open spin chain with diagonal boundary fields has the symmetry U_q (SU(L)) x U_q (SU(N-L)) x U(1), as well as a ``duality'' symmetry which interchanges L and N - L. We exploit these symmetries to compute exact boundary S matrices in the regime with q real.