Bosonic and Fermionic Eigenstates for Generalized Sutherland Models
Akinori Nishino, Miki Wadati
Abstract
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.
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