Representation zeta functions of groups of type A2 in positive characteristic
Abstract
We prove two conjectures regarding the representation growth of groups of type A2. 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 A2 in positive characteristic assuming Serre's conjecture on the congruence subgroup problem.
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