Representations lisses de GL(m,D), IV : representations supercuspidales

摘要

Let F be a non Archimedean locally compact field and let D be a centralF-division algebra. We prove that any positive level supercuspidal irreduciblerepresentation of the group GL(m,D) is compactly induced from a representationof a compact mod center open subgroup of GL(m,D). More precisely, we prove thatsuch representations contain a maximal simple type.