Kazhdan constants for Chevalley groups over the integers

  • Marek Kaluba

    Karlsruhe Institute of Technology, Karlsruhe, Germany
  • Dawid Kielak

    University of Oxford, Oxford, UK
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Abstract

We compute lower bounds for Kazhdan constants of Chevalley groups over the integers, endowed with the standard Steinberg generators. For types other than , 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.

Cite this article

Marek Kaluba, Dawid Kielak, Kazhdan constants for Chevalley groups over the integers. Rev. Mat. Iberoam. 41 (2025), no. 4, pp. 1253–1269

DOI 10.4171/RMI/1534