
Journal of Lie Theory 19 (2009), No. 1, 029054 Copyright Heldermann Verlag 2009 Comparison of Lattice Filtrations and MoyPrasad Filtrations for Classical Groups Bertrand Lemaire Institut de Mathématiques, Université AixMarseille II, 163 Av. de Luminy, 13288 Marseille 9, France lemaire@iml.univmrs.fr [Abstractpdf] \def\g{{\frak g}} \def\R{{\Bbb R}} Let $F_\circ$ be a nonArchimedean local field of characteristic not $2$. Let $G$ be a classical group over $F_\circ$ which is not a general linear group, i.e. a symplectic, orthogonal or unitary group over $F_\circ$ (possibly with a skewfield involved). Let $x$ be a point in the building of $G$. In this article, we prove that the lattice filtration $(\g_{x,r})_{r\in\R}$ of $\g={\rm Lie}(G)$ attached to $x$ by Broussous and Stevens, coincides with the filtration defined by Moy and Prasad. Keywords: Local field, division algebra, classical group, building, lattice filtration, MoyPrasad filtration, unramified descent. MSC: 20G25, 11E57 [ Fulltextpdf (288 KB)] for subscribers only. 