On a decomposition of $p$-adic Coxeter orbits
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866918523990704128 |
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| author | Ivanov, Alexander B. |
| author_facet | Ivanov, Alexander B. |
| contents | We analyze the geometry of some $p$-adic Deligne--Lusztig spaces $X_w(b)$ introduced in [Iva21] attached to an unramified reductive group ${\bf G}$ over a non-archimedean local field. We prove that when ${\bf G}$ is classical, $b$ basic and $w$ Coxeter, $X_w(b)$ decomposes as a disjoint union of translates of a certain integral $p$-adic Deligne--Lusztig space. Along the way we extend some observations of DeBacker and Reeder on rational conjugacy classes of unramified tori to the case of extended pure inner forms, and prove a loop version of Frobenius-twisted Steinberg's cross section. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_01424 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On a decomposition of $p$-adic Coxeter orbits Ivanov, Alexander B. Algebraic Geometry Representation Theory 20G25, 14M15 (primary), 14F20 (secondary) We analyze the geometry of some $p$-adic Deligne--Lusztig spaces $X_w(b)$ introduced in [Iva21] attached to an unramified reductive group ${\bf G}$ over a non-archimedean local field. We prove that when ${\bf G}$ is classical, $b$ basic and $w$ Coxeter, $X_w(b)$ decomposes as a disjoint union of translates of a certain integral $p$-adic Deligne--Lusztig space. Along the way we extend some observations of DeBacker and Reeder on rational conjugacy classes of unramified tori to the case of extended pure inner forms, and prove a loop version of Frobenius-twisted Steinberg's cross section. |
| title | On a decomposition of $p$-adic Coxeter orbits |
| topic | Algebraic Geometry Representation Theory 20G25, 14M15 (primary), 14F20 (secondary) |
| url | https://arxiv.org/abs/2109.01424 |