From affine Hecke algebras to boundary symmetries
Résumé
Solutions of the reflection equation for the $U_{q}(\hat{sl_n})$ case are obtained by implementing certain realizations of the affine Hecke algebra. The boundary non-local charges associated to non-diagonal solutions of the reflection equation are constructed systematically, and the symmetry of the corresponding open spin chain is investigated. We prove that the symmetry of the open spin chain is essentially a remnant of the $U_{q}(gl_{n})$ algebra.