Spectral gap and character limits in arithmetic groups

Arie Levit; Raz Slutsky; Itamar Vigdorovich

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arXiv · 2308.05562

Spectral gap and character limits in arithmetic groups

Arie Levit·Raz Slutsky·Itamar Vigdorovich

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Abstract

We establish vanishing results for limits of characters in various discrete groups, most notably irreducible lattices in higher rank semisimple Lie groups. As an application, we show that any sequence of finite-dimensional representations converges to the regular representation in the Fell topology. We achieve this by studying the geometry of the simplex of traces of discrete groups having Kazhdan's property (T) or its relative generalizations.

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Arie Levit, Raz Slutsky, Itamar Vigdorovich. 2023-08-10. Spectral gap and character limits in arithmetic groups. https://arxiv.org/abs/2308.05562

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