Bosonic and Fermionic Eigenstates for Generalized Sutherland Models

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.

20 pages, LaTeX

References in corpus (3)

• Lectures on Dunkl operators
• Rodrigues Formula for the Nonsymmetric Multivariable Hermite Polynomial
• Rodrigues Formula for the Nonsymmetric Multivariable Laguerre Polynomial

Cited by in corpus (3)

• On the evaluation formula for Jack polynomials with prescribed symmetry
• Algebraic study on the $A_{N-1}$- and $B_N$-Calogero models with bosonic, fermionic and distinguishable particles
• Equivalence of the super Lax and local Dunkl operators for Calogero-like models