Journal of Lie Theory

no. 1
Comparison of Lattice Filtrations and Moy-Prasad Filtrations for Classical Groups
Journal of Lie Theory, Volume 19 (2009) no. 1, pp. 29-54
\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.
DOI: 10.5802/jolt.540
Classification: 20G25, 11E57
Keywords: Local field, division algebra, classical group, building, lattice filtration, Moy-Prasad filtration, unramified descent 
@article{JOLT_2009_19_1_a1,
     author = {B. Lemaire},
     title = {Comparison of {Lattice} {Filtrations} and {Moy-Prasad} {Filtrations} for {Classical} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {29--54},
     year = {2009},
     volume = {19},
     number = {1},
     doi = {10.5802/jolt.540},
     zbl = {1178.20044},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.540/}
}
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B. Lemaire. Comparison of Lattice Filtrations and Moy-Prasad Filtrations for Classical Groups. Journal of Lie Theory, Volume 19 (2009) no. 1, pp. 29-54. doi: 10.5802/jolt.540

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