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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.13027 |
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| _version_ | 1866912903326597120 |
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| author | Petschick, J. Moritz Piccolo, Margherita |
| author_facet | Petschick, J. Moritz Piccolo, Margherita |
| contents | We consider the representation growth of split extensions of $SL_2^m(O)$. We prove that the corresponding representation zeta functions factor as a product of the representation zeta function of $SL_2^m(O)$ and the relative representation zeta function associated to the extension. We make use of our result by computing the zeta functions for two infinite families of split extensions of $SL_2^m(O)$ explicitly. Along the way, we compute the representation zeta functions of a large class of subgroups of $SL_2^m(O)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13027 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Representation zeta functions of split extensions of $SL_2^m(O)$ Petschick, J. Moritz Piccolo, Margherita Group Theory Representation Theory 22E50, 11M41 (Primary) 20F69, 20C15 (Secondary) We consider the representation growth of split extensions of $SL_2^m(O)$. We prove that the corresponding representation zeta functions factor as a product of the representation zeta function of $SL_2^m(O)$ and the relative representation zeta function associated to the extension. We make use of our result by computing the zeta functions for two infinite families of split extensions of $SL_2^m(O)$ explicitly. Along the way, we compute the representation zeta functions of a large class of subgroups of $SL_2^m(O)$. |
| title | Representation zeta functions of split extensions of $SL_2^m(O)$ |
| topic | Group Theory Representation Theory 22E50, 11M41 (Primary) 20F69, 20C15 (Secondary) |
| url | https://arxiv.org/abs/2602.13027 |