Kazhdan constants for Chevalley groups over the integers

2024/11/14 by Marek Kaluba, Dawid Kielak · 1 citation

paper · doi:10.4171/rmi/1534

published in Revista Matemática Iberoamericana 41(4), 1253-1269 (European Mathematical Society - EMS - Publishing House GmbH)

crossref issued 2024/11/14 · crossref published 2024/11/14 · crossref published-print 2024/11/14 · crossref created 2024/11/14 · crossref deposited 2026/06/30 · crossref indexed 2026/07/30

Abstract

We compute lower bounds for Kazhdan constants of Chevalley groups over the integers, endowed with the standard Steinberg generators. For types other than \mathttA_n , these are the first explicit asymptotically sharp such bounds. The method relies on establishing a new connection between the structure of a root system grading a family of groups and the behaviour of the square of the Laplace operator in the family.

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