On a decomposition of $p$-adic Coxeter orbits
On a decomposition of $p$-adic Coxeter orbits
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 …