A generalized Macdonald operator
Representation Theory
2011-08-30 v1 Combinatorics
Abstract
We present an explicit difference operator diagonalized by the Macdonald polynomials associated with an (arbitrary) admissible pair of irreducible reduced crystallographic root systems. By the duality symmetry, this gives rise to an explicit Pieri formula for the Macdonald polynomials in question. The simplest examples of our construction recover Macdonald's celebrated difference operators and associated Pieri formulas pertaining to the minuscule and quasi-minuscule weights. As further by-products, explicit expansions and Littlewood-Richardson type formulas are obtained for the Macdonald polynomials associated with a special class of small weights.
Cite
@article{arxiv.1009.4486,
title = {A generalized Macdonald operator},
author = {J. F. van Diejen and E. Emsiz},
journal= {arXiv preprint arXiv:1009.4486},
year = {2011}
}
Comments
11 pages. To appear in Int. Math. Res. Not. IMRN