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# What is a canonocalcanonical set of representatives in $GL(n,F)$ for the vertices in the Bruhat Tits building?

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$F$ is a non archimedean field here. To be more precise, I would actually prefer a set of representative in $B(F)$ for the discrete space $B(F) / B(o)Z(F)$?

This can be phrased also as question about lattices in $F^n$, but I would prefer to stay on the group level.

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# What is a canonocal set of representatives in $GL(n,F)$ for the vertices in the Bruhat Tits building?

$F$ is a non archimedean field here. To be more precise, I would actually prefer a set of representative in $B(F)$ for the discrete space $B(F) / B(o)Z(F)$?