Rodrigues formulas for the non-symmetric multivariable polynomials associated with the BCN-type root system Original Research Article

The non-symmetric Macdonald–Koornwinder polynomials are joint eigenfunctions of the commuting Cherednik operators which are constructed from the representation theory for the affine Hecke algebra corresponding to the BCN-type root system. We present the Rodrigues formula for the non-symmetric Macdonald–Koornwinder polynomials. The raising operators are derived from the realizations of the corresponding double affine Hecke algebra. In the quasi-classical limit, the above theory reduces to that of the BCN-type Sutherland model which describes many particles with inverse-square long-range interactions on a circle with one impurity. We also present the Rodrigues formula for the non-symmetric Jacobi polynomials of type BCN which are eigenstates of the BCN-type Sutherland model.