Abstract:
Many special properties of the Haldane-Shastry long-range spin chain naturally arise from a connection with the spin Calogero–Sutherland model. This connection is established by so-called «freezing trick». The $q$-deformed Haldane-Shastry model was constructed by D. Uglov via freezing from the affine Hecke algebra. The $q$-deformed case is connected with the spin trigonometric Macdonald-Ruijsenaars operators, which explicit expressions were presented in recent works By J. Lamers, V. Pasquier and D. Serban. We introduce the elliptic q-deformed anisotropic long-range spin chain. The derivation is based on our recent construction for commuting anisotropic elliptic spin Macdonald-Ruijsenaars operators.
