Corpus ID: 1614277

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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Even Galois representations and the cohomology of GL(2,Z)
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References

SHOWING 1-6 OF 6 REFERENCES
Convexity and Commuting Hamiltonians
  • 843
  • PDF
Kostant convexity for affine buildings
  • 8
  • Highly Influential
  • PDF
On convexity, the Weyl group and the Iwasawa decomposition
  • 322
  • PDF
Spherical functions on a group of p-adic type
  • 256
editors), Galois representations in arithmetic algebraic geometry , proceedings of a conference in Durham, 1996
  • Volume 254 in the London Mathematical Society Lecture Note Series Cambridge University Press,
  • 1998