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We construct bosonic and fermionic eigenstates for the generalized Sutherlandmodels associated with arbitrary reduced root systems respectively, throughW-symmetrization and W-anti-symmetrization of Heckman-Opdam's nonsymmetricJacobi polynomials. Square norms of the nonsymmetric Heckman-Opdam polynomialsare evaluated from their Rodrigues formulae. The W-symmetrization andW-anti-symmetrization of the nonsymmetric polynomials enable us to evaluatesquare norms of bosonic and fermionic eigenstates for the generalizedSutherland models.Comment: 20 pages, LaTe

Bosonic and fermionic eigenstates for generalized Sutherland models