Earlier this year at IPhT, I presented a new and simpler expression for Uglov's Hamiltonian of the $q$-deformed Haldane–Shastry model, a long-range spin chain enjoying quantum-affine symmetries already at finite system size. After reviewing the model I will present its (conjectural) exact (highest-weight) eigenvectors, whose wave functions are essentially a $q$-Vandermonde factor squared, times a Macdonald polynomial (with $t=q^2$), “decorated'' by some Hecke generators. This is ongoing work together with Vincent Pasquier and Didina Serban.

Stockholm