Correspondance de Howe et sous-groupes parahoriques.
Dans cet article, nous proposons une nouvelle méthode pour démontrer la bijectivité de la correspondance de Howe pour les paires duales du type sur un corps localement compact non archimédien. La preuve est basée sur une étude soigneuse de la filtration de Kudla [11] ainsi que sur les résultats de [13] à propos de l’irréductibilité d’une représentation induite parabolique. Elle est valable pour de caractéristique quelconque et nous permet d’expliciter la bijection en termes des paramètres...
Let be a -adic field, and let endowed with the Haar measure determined by giving a maximal compact subgroup measure . Let denote the number of conjugacy classes of arithmetic lattices in with co-volume bounded by . We show that under the assumption that does not contain the element , where denotes the -th root of unity over , we have where denotes the order of the residue field of .
Gruenhage asked if it was possible to cover the real line by less than continuum many translates of a compact nullset. Under the Continuum Hypothesis the answer is obviously negative. Elekes and Stepr mans gave an affirmative answer by showing that if is the well known compact nullset considered first by Erdős and Kakutani then ℝ can be covered by cof() many translates of . As this set has no analogue in more general groups, it was asked by Elekes and Stepr mans whether such a result holds for...
This survey on crystallographic groups, geometric structures on Lie groups and associated algebraic structures is based on a lecture given in the Ostrava research seminar in .