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The centralizer of a classical group and Bruhat-Tits buildings

Daniel Skodlerack,
published 2011-02-01

We consider the embedding of the building of the centralizer H of a semisimple rational Lie algebra element in a classical group G into the building of G in such a way such that the map respects the Moy-Prasad filtration. We show that the last property implies uniqueness up to translations and uniqueness in some casses. The whole work is done over a non-Archimedean local field of residue characteristic not 2.

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