Alexander B. Ivanov - On a decomposition of $p$-adic Coxeter orbits

epiga:8562 - Épijournal de Géométrie Algébrique, September 27, 2023, Volume 7 -
On a decomposition of $p$-adic Coxeter orbitsArticle

Authors: Alexander B. Ivanov

    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.

    Volume: Volume 7
    Published on: September 27, 2023
    Accepted on: June 9, 2023
    Submitted on: October 8, 2021
    Keywords: Mathematics - Algebraic Geometry,Mathematics - Representation Theory,20G25, 14M15 (primary), 14F20 (secondary)

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