An algebraic study on the A(N-1)- and B-N-Calogero models with bosonic, fermionic and distinguishable particles

Through an algebraic method using the Dunkl-Cherednik operators, the multiv ariable Hermite and Laguerre polynomials associated with the A(N-1)-and B-N -Calogero models with bosonic, fermionic and distinguishable particles are investigated. The Rodrigues formulae of column type that algebraically gene rate the monic non-symmetric multivariable Hermite and Laguerre polynomials corresponding to the distinguishable case are presented. Symmetric and ant i-symmetric polynomials that respectively give the eigenstates for bosonic and fermionic particles are also presented by the symmetrization and anti-s ymmetrization of the non-symmetric ones. The norms of all the eigenstates f or all cases are algebraically calculated in a unified way.