Kazhdan constants for Chevalley groups over the integers

Marek Kaluba; Dawid Kielak

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arXiv · 2306.12358

Kazhdan constants for Chevalley groups over the integers

Marek Kaluba·Dawid Kielak

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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 $\mathtt{A}_{n}$, 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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Marek Kaluba, Dawid Kielak. 2023-06-21. Kazhdan constants for Chevalley groups over the integers. https://arxiv.org/abs/2306.12358

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