THE COHOMOLOGY OF p-ADIC DELIGNE-LUSZTIG SCHEMES OF COXETER TYPE

We determine the cohomology of the closed Drinfeld stratum of p-adic Deligne-Lusztig schemes of Coxeter type attached to arbitrary inner forms of unramified groups over a local non-archimedean field. We prove that the corresponding torus weight spaces are supported in exactly one cohomological degree and are pairwise non-isomorphic irreducible representations of the pro-unipotent radical of the corresponding parahoric subgroup. We also prove that all Moy-Prasad quotients of this stratum are maximal varieties, and we investigate the relation between the resulting representations and Kirillov's orbit method.