Fake degrees for reflection actions on roots
Combinatorics
2012-01-30 v2
Abstract
A finite irreducible real reflection group of rank l and Coxeter number h has root system of cardinality h*l. It is shown that the fake degree for the permutation action on its roots is divisible by [h]_q = 1+q+q^2+...+q^{h-1}, and that in simply-laced types, it equals [h]_q times the summation of q^{e_i - 1} where e_i runs through the exponents, so that e_i - 1 are the codegrees.
Keywords
Cite
@article{arxiv.1201.0032,
title = {Fake degrees for reflection actions on roots},
author = {Victor Reiner and Zhiwei Yun},
journal= {arXiv preprint arXiv:1201.0032},
year = {2012}
}
Comments
Added discussion of overlap with prior work by J. Stembridge