Creation operators for the Macdonald and Jack polynomials (Q1362372): Difference between revisions

In a previous paper [\textit{L. Lapointe} and \textit{L. Vinet} in Int. Math. Res. 1995, No. 9, 419-424 (1995; Zbl 0868.33009)] the authors constructed Jack polynomials by means of creation operators acting on the identity. Since Jack polynomials are a specialization of Macdonald polynomials, a similar problem is considered here. A Rodrigues-type formula is derived, expressing a Macdonald polynomial as a string of creation operators acting on the identity. The present construction is however different from the one for Jack polynomials. In terms of the creation operators some conjectures are formulated which imply that the expansion coefficients of the Macdonald polynomials in the monomial basis are polynomials with integer coefficients.