English

c-functions and Macdonald polynomials

Combinatorics 2022-12-08 v1 Representation Theory

Abstract

This is a paper about cc-functions and Macdonald polynomials. There are cc-function formulas for EE-expansions of PλP_\lambda and Aλ+ρA_{\lambda+\rho}, principal specializations of PλP_\lambda and EμE_\mu, for Macdonald's constant term formulas, and for the norms of Macdonald polynomials. Most of these follow from the creation formulas for Macdonald polynomials, providing alternative proofs to several results from Macdonald (2003). In addition, we prove the Boson-Fermion correspondence in the Macdonald polynomial setting and the Weyl character formula for Macdonald polynomials.

Keywords

Cite

@article{arxiv.2212.03312,
  title  = {c-functions and Macdonald polynomials},
  author = {Laura Colmenarejo and Arun Ram},
  journal= {arXiv preprint arXiv:2212.03312},
  year   = {2022}
}
R2 v1 2026-06-28T07:24:11.570Z