Spectral gap and character limits in arithmetic groups
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866929387567316992 |
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| author | Levit, Arie Slutsky, Raz Vigdorovich, Itamar |
| author_facet | Levit, Arie Slutsky, Raz Vigdorovich, Itamar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_05562 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spectral gap and character limits in arithmetic groups Levit, Arie Slutsky, Raz Vigdorovich, Itamar Group Theory Operator Algebras 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. |
| title | Spectral gap and character limits in arithmetic groups |
| topic | Group Theory Operator Algebras |
| url | https://arxiv.org/abs/2308.05562 |