Bosonic and Fermionic Eigenstates for Generalized Sutherland Models

We construct bosonic and fermionic eigenstates for the generalized Sutherland models associated with arbitrary reduced root systems respectively, through W-symmetrization and W-anti-symmetrization of Heckman-Opdam’s nonsymmetric Jacobi polynomials. Square norms of the nonsymmetric Heckman-Opdam polynomials are evaluated from their Rodrigues formulae. The W-symmetrization and W-anti-symmetrization of the nonsymmetric polynomials enable us to evaluate square norms of bosonic and fermionic eigenstates for the generalized Sutherland models.