Representation Zeta Functions of Groups of Type A2 in Positive Characteristic

Uri Onn; Amritanshu Prasad; Pooja Singla

doi:10.1093/imrn/rnae270

Representation Zeta Functions of Groups of Type A₂ in Positive Characteristic

Uri Onn
, Amritanshu Prasad
, Pooja Singla

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 universality 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 property.

Original language	English
Article number	rnae270
Journal	International Mathematics Research Notices
Volume	2025
Issue number	2
DOIs	https://doi.org/10.1093/imrn/rnae270
State	Published - 1 Jan 2025
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1093/imrn/rnae270

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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 universality of representation zeta functions over local complete discrete valuation rings. The second is the Larsen{\textendash}Lubotzky conjecture on the representation growth of irreducible lattices in groups of type A2 in positive characteristic, assuming Serre{\textquoteright}s conjecture on the congruence subgroup property.",

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AB - We prove two conjectures regarding the representation growth of groups of type A2. The first, conjectured by Avni, Klopsch, Onn, and Voll, regards the universality 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 property.

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Representation Zeta Functions of Groups of Type A₂ in Positive Characteristic

Abstract

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