Duality and quantum-algebra symmetry of the AN−1 (1) open spin chain with diagonal boundary fields

Abstract

We show that the transfer matrix of the A N−1 (1) open spin chair with diagonal boundary fields has the symmetry U q ( SU( l)) × U q ( SU( N− l)) × U(1), as well as a “duality” symmetry which maps l ↔ N − l. We exploit these symmetries to compute exact boundary S-matrices in the regime with q real.