Character stacks are PORC count
Representation Theory
2022-09-16 v2 Algebraic Geometry
Number Theory
Abstract
We compute the number of points over finite fields of the character stack associated to a compact surface group and a reductive group with connected centre. We find that the answer is a Polynomial On Residue Classes (PORC). The key ingredients in the proof are Lusztig's Jordan decomposition of complex characters and Deriziotis's results on genus numbers of finite reductive groups. As a consequence of our main theorem, we obtain an expression for the -polynomial of the character stack.
Cite
@article{arxiv.2203.04521,
title = {Character stacks are PORC count},
author = {Nick Bridger and Masoud Kamgarpour},
journal= {arXiv preprint arXiv:2203.04521},
year = {2022}
}
Comments
21 Pages. Minor changes since last submission. To appear in the Journal of the Australian Math Society