English

Representation zeta functions of groups of type $A_2$ in positive characteristic

Representation Theory 2024-05-02 v2

Abstract

We prove two conjectures regarding the representation growth of groups of type A2A_2. The first, conjectured by Avni, Klopsch, Onn and Voll, regards the uniformity of representation zeta functions over local complete discrete valuation rings. The second is the Larsen--Lubotzky conjecture on the representation growth of irreducible lattices in groups of type A2A_2 in positive characteristic assuming Serre's conjecture on the congruence subgroup problem.

Keywords

Cite

@article{arxiv.2308.07073,
  title  = {Representation zeta functions of groups of type $A_2$ in positive characteristic},
  author = {Uri Onn and Amritanshu Prasad and Pooja Singla},
  journal= {arXiv preprint arXiv:2308.07073},
  year   = {2024}
}