What is the Iwahori subgroup for $PGL_2(F)$ where $F$ is a local field? I am also looking for the Levi subgroups but it seems that there is only 1 levi subgroup been the identity but this seems odd to me.
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The (standard) Iwahori $\bar I$ of ${\rm PGL}(N,F)$ is the image of the Iwahori subgroup $I$ of ${\rm GL}(N,F)$ formed of the matrices with integer coefficients, upper triangular mod ${\mathfrak p}_F$, and with invertible determinant. To extract its defition from BruhatTits general theory, there is an extra difficulty here coming from the fact that the group is not simply connected (contrary to e.g. ${\rm SL}(N,F)$). 

