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arXiv · 2109.01424

On a decomposition of $p$-adic Coxeter orbits

Alexander B. Ivanov
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Abstract

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.

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Alexander B. Ivanov. 2021-09-03. On a decomposition of $p$-adic Coxeter orbits. https://doi.org/10.46298/epiga.2023.8562

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