Kostant convexity for affine buildings

@inproceedings{Hitzelberger2010KostantCF,
  title={Kostant convexity for affine buildings},
  author={Petra Hitzelberger},
  year={2010}
}
We prove an analogue of Kostant’s convexity theorem for thick affine buildings and give an application for groups with affine BN -pairs. Recall that there are two natural retractions of the affine building onto a fixed apartment A: The retraction r centered at an alcove in A and the retraction ρ centered at a chamber in the spherical building at infinity. We prove that for each special vertex x ∈ A the set ρ(r−1(W .x)) is a certain convex hull of W .x . The proof can be reduced to a statement… CONTINUE READING