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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.20773 |
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| _version_ | 1866909554183241728 |
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| author | Sela, Orit Schaps, Mary Vishne, Uzi |
| author_facet | Sela, Orit Schaps, Mary Vishne, Uzi |
| contents | We consider quotients of the Bruhat-Tits building associated to the projective linear groups of dimension $d>2$ over the function field $\mathbb F_q(t)$ by a non-uniform lattice $Γ$ which is a congruence subgroup in the non-uniform lattice $ PGL_{d}(R)$, where $R=\mathbb F_q[\frac{1}{t}]$. We determine a fundamental domain and demonstrate that the quotient, while not cofinite, is at least of finite covolume. We do the case $d=3$ in considerable detail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20773 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quotients of Buildings by Non-uniform Lattices Sela, Orit Schaps, Mary Vishne, Uzi Representation Theory Group Theory Primary: 22K55, Secondary, 20E42 We consider quotients of the Bruhat-Tits building associated to the projective linear groups of dimension $d>2$ over the function field $\mathbb F_q(t)$ by a non-uniform lattice $Γ$ which is a congruence subgroup in the non-uniform lattice $ PGL_{d}(R)$, where $R=\mathbb F_q[\frac{1}{t}]$. We determine a fundamental domain and demonstrate that the quotient, while not cofinite, is at least of finite covolume. We do the case $d=3$ in considerable detail. |
| title | Quotients of Buildings by Non-uniform Lattices |
| topic | Representation Theory Group Theory Primary: 22K55, Secondary, 20E42 |
| url | https://arxiv.org/abs/2503.20773 |