Explicit vertex-operator super-Hamiltonians are conjectured whose eigenfunctions are the super-Macdonald polynomials of earlier work.
The supersymmetric Ruijsenaars-Schneider model
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An integrable supersymmetric generalization of the trigonometric Ruijsenaars-Schneider model is presented whose symmetry algebra includes the super Poincar\'e algebra. Moreover, its Hamiltonian is showed to be diagonalized by the recently introduced Macdonald superpolynomials. Somewhat surprisingly, the consistency of the scalar product forces the discreteness of the Hilbert space.
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Super-Hamiltonians for super-Macdonald polynomials
Explicit vertex-operator super-Hamiltonians are conjectured whose eigenfunctions are the super-Macdonald polynomials of earlier work.