Resumen de Intégrabilité locale des caractères de SLn(D)

Bertrand Lemaire

• Let F be a nonarchimedean locally compact field, G be the multiplicative group of a finite dimensional central simple F-algebra, and G' be the kernel of the reduced norm det' : G ? F×. We prove in this paper that for all distinguished open subgroup H ? G and all irreducible (smooth complex) representation p of H, the character Tp = trace(p) is a locally integrable distribution on H, locally constant on the set of regular elements of H. Then we deduce that for all irreducible representation p' of G', the character Tp' = trace(p') is a locally integrable distribution on G', locally constant on the set of regular elements of G'.