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Journal of Lie Theory 19 (2009), No. 1, 029--054
Copyright Heldermann Verlag 2009

Comparison of Lattice Filtrations and Moy-Prasad Filtrations for Classical Groups

Bertrand Lemaire
Institut de Mathématiques, Université Aix-Marseille II, 163 Av. de Luminy, 13288 Marseille 9, France


\def\g{{\frak g}} \def\R{{\Bbb R}} Let $F_\circ$ be a non-Archimedean 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 skew-field 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, Moy-Prasad filtration, unramified descent.

MSC: 20G25, 11E57

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