Cartan limits of SL(n, Q_p) (Corina Ciobotaru, Fribourg)

07.11.2017 10:30

For a locally compact group G the set of all its closed subgroups S(G) is endowed with the Chabauty topology, under which S(G) becomes a compact space. Given a family of closed subgroups of G satisfying some properties it is then natural to ask if its limit subgroups in S(G) preserve the same properties and if we can explicitly compute them.

In a recent joint work with Arielle Leitner we study the limits under the Chabauty topology of Cartan subgroups of SL(n,Q_p), the closed subgroups SL(n, Q_p)-conjugated to the diagonal subgroup of SL(n, Q_p). When a limit subgroup contains only elliptic elements we prove that up to conjugacy it is contained in the unipotent radical of the Borel subgroup of SL(n,Q_p). The key idea is an explicit homeomorphism between the Chabauty closure of Cartan sub-algebras of sl(n, Q_p) and the Chabauty closure of Cartan subgroups of SL(n,Q_p). By the Flat Torus Theorem when a limit subgroup contains hyperbolic elements we prove it preserves a flat, not necessary of maximal dimension, in the Bruhat-Tits building associated with SL(n,Q_p).

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Room 623, Séminaire "Groupes et Géométrie"

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