On $e$-local structures for $\mathbb{Z}_\ell$-spetses
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914909943496704 |
|---|---|
| author | Rossi, Damiano Semeraro, Jason |
| author_facet | Rossi, Damiano Semeraro, Jason |
| contents | Let $q$ be a prime power, $\ell$ a prime not dividing $q$, and $e$ the order of $q$ modulo $\ell$. We show that the geometric realisation of the nerve of the transporter category of $e$-split Levi subgroups of a finite reductive group $G$ over $\mathbb{F}_q$ is homotopy equivalent to the classifying space $BG$ up to $\ell$-completion. We suggest a generalisation of this equivalence to the setting of $\mathbb{Z}_\ell$-reflection cosets and establish a related fact involving the associated orbit spaces. We also establish a Dade-like formula for unipotent characters of $\mathbb{Z}_\ell$-spetses inspired by a question of Broué. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06132 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On $e$-local structures for $\mathbb{Z}_\ell$-spetses Rossi, Damiano Semeraro, Jason Group Theory Representation Theory 20C15, 55P10, 55R35 Let $q$ be a prime power, $\ell$ a prime not dividing $q$, and $e$ the order of $q$ modulo $\ell$. We show that the geometric realisation of the nerve of the transporter category of $e$-split Levi subgroups of a finite reductive group $G$ over $\mathbb{F}_q$ is homotopy equivalent to the classifying space $BG$ up to $\ell$-completion. We suggest a generalisation of this equivalence to the setting of $\mathbb{Z}_\ell$-reflection cosets and establish a related fact involving the associated orbit spaces. We also establish a Dade-like formula for unipotent characters of $\mathbb{Z}_\ell$-spetses inspired by a question of Broué. |
| title | On $e$-local structures for $\mathbb{Z}_\ell$-spetses |
| topic | Group Theory Representation Theory 20C15, 55P10, 55R35 |
| url | https://arxiv.org/abs/2408.06132 |