Intégrabilité locale des caractères de SLn(D)

• Autores: Bertrand Lemaire
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 222, Nº 1, 2005, págs. 69-132
• Idioma: inglés
• DOI: 10.2140/pjm.2005.222.69
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• Resumen

  • 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'.