I have a basic question/ clarification required about Bruhat-Tits buildings of the groups of $GL_n$, $PGL_n$ and $SL_n$ over say a finite extension of $\mathbb{Q}_p$. I have seen in different documents the groups $PGL_n$ and $SL_n$ being used interchangeably to define the same Bruhat-Tits building, using lattice chains for example (Can't think of good references off the top of my head, but I can try to have exact references if required). But I have also heard people say that there are subtle differences between these. Can someone explain or point out a reference where the examples of these groups and their differences (if any) are discussed?
2025-01-14 11:38:09.1736854689
Difference in Bruhat-Tits Building of $PGL_n$ and $SL_n$
133 Views Asked by Aranya Lahiri https://math.techqa.club/user/aranya-lahiri/detail AtRelated Questions in REPRESENTATION-THEORY
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