Monk rules for type $GL_n$ Macdonald polynomials
Combinatorics
2022-12-09 v1 Representation Theory
Abstract
In this paper we give Monk rules for Macdonald polynomials which are analogous to the Monk rules for Schubert polynomials. These formulas are similar to the formulas given by Baratta (2008), but our method of derivation is to use Cherednik's interwiners. Deriving Monk rules by this technique addresses the relationship between the work of Baratta and the product formulas of Yip (2010). Specializations of the Monk formula's at and/or provide Monk rules for Iwahori-spherical polynomials and for finite and affine key polynomials.
Keywords
Cite
@article{arxiv.2212.04032,
title = {Monk rules for type $GL_n$ Macdonald polynomials},
author = {Tom Halverson and Arun Ram},
journal= {arXiv preprint arXiv:2212.04032},
year = {2022}
}