Geodesic
On a decomposition of $p$-adic Coxeter orbits
Épijournal de Géométrie Algébrique, Tome 7 (2023)

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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.
DOI : 10.46298/epiga.2023.8562
Classification : 14F20, 14M15, 20G25 
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     author = {Ivanov, Alexander B.},
     title = {On a decomposition of $p$-adic {Coxeter} orbits},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
     publisher = {mathdoc},
     volume = {7},
     year = {2023},
     doi = {10.46298/epiga.2023.8562},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2023.8562/}
}
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Ivanov, Alexander B. On a decomposition of $p$-adic Coxeter orbits. Épijournal de Géométrie Algébrique, Tome 7 (2023). doi: 10.46298/epiga.2023.8562

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