Spectral gap and character limits in arithmetic groups

2023/08/10 by Arie Levit, Raz Slutsky, Levit, Arie +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Mathematical Analysis and Transform Methods #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2308.05562

openalex publication_date 2023/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Hyperlinearity, stability and asymptotic spectral gap of higher rank lattices

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