# The Bruhat-Tits tree of SL ( 2 )

@inproceedings{Casselman2016TheBT, title={The Bruhat-Tits tree of SL ( 2 )}, author={B. Casselman}, year={2016} }

and preserves the open cone C of positive definite matrices. The quotient PGL2(R) = GL2(R)/{scalars} therefore acts on the space P(C), the space of such matrices modulo positive scalars. In effect, P(C) parametrizes the shapes of ellipses in the plane. The isotropy subgroup of I is the image O(2) = O(2)/{±I} in PGL2(R), so that P(C) may be identified with PGL2(R)/O(2). The embedding of SL2 into GL2 identifies this with SL2(R)/SO(2).

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