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The centralizer of a classical group and Bruhat-Tits buildings

Daniel Skodlerack — 2013

Annales de l’institut Fourier

Let G be a unitary group defined over a non-Archimedean local field of odd residue characteristic and let H be the centralizer of a semisimple rational Lie algebra element of G . We prove that the Bruhat-Tits building 𝔅 1 ( H ) of H can be affinely and G -equivariantly embedded in the Bruhat-Tits building 𝔅 1 ( G ) of G so that the Moy-Prasad filtrations are preserved. The latter property forces uniqueness in the following way. Let j and j be maps from 𝔅 1 ( H ) to 𝔅 1 ( G ) which preserve the Moy–Prasad filtrations. We prove that...

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