From affine Hecke algebras to boundary symmetries

Dan Lévy

Nir Sochen

A.P. Isaev, O. Ogievetsky, A.F. Os'kin

Anastasia Doikou

Solutions of the reflection equation for the Uq ( sln) case are obtained by implementing certain realisations of the affine Hecke algebra. The boundary non–local charges associated to nondiagonal 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 Uq(gln) algebra.

A. Babichenko, Vidas Regelskis

We construct boundary type operators satisfying fused reflection equation for arbitrary representations of the Baxterized affine Hecke algebra. These operators are analogues of the fused reflection matrices in solvable half-line spin chain models. We show that these operators lead to a family of commuting transfer matrices of Sklyanin type. We derive fusion type functional relations for these operators for two families of representations.

Anastasia Doikou