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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.06996 |
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| _version_ | 1866918193668292608 |
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| author | Wolf, Lasse Lennart |
| author_facet | Wolf, Lasse Lennart |
| contents | Given a real semisimple Lie group $G$ with finite center and a discrete subgroup $Γ\subset G$ whose limit cone is disjoint from two facets of the Weyl chamber we show that Quint's growth indicator function $ψ_Γ$ is bounded by the half sum of positive roots $ρ$, i.e. it has slow growth, implying that the representation $L^2(Γ\backslash G)$ is tempered. In particular, this holds for each $I$-Anosov subgroup provided that $I$ contains at least two distinct simple roots that are not interchanged by the opposition involution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06996 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The limit cone and bounds on the growth indicator function Wolf, Lasse Lennart Representation Theory Group Theory Spectral Theory Given a real semisimple Lie group $G$ with finite center and a discrete subgroup $Γ\subset G$ whose limit cone is disjoint from two facets of the Weyl chamber we show that Quint's growth indicator function $ψ_Γ$ is bounded by the half sum of positive roots $ρ$, i.e. it has slow growth, implying that the representation $L^2(Γ\backslash G)$ is tempered. In particular, this holds for each $I$-Anosov subgroup provided that $I$ contains at least two distinct simple roots that are not interchanged by the opposition involution. |
| title | The limit cone and bounds on the growth indicator function |
| topic | Representation Theory Group Theory Spectral Theory |
| url | https://arxiv.org/abs/2511.06996 |