Kostant convexity for affine buildings

Petra Hitzelberger
2010 Forum mathematicum  
We prove an analogue of Kostants convexity theorem for thick affine buildings and give an application for groups with affine BN -pair. 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 problem in
more » ... ter complexes and heavily relies on a character formula for highest weight representations of algebraic groups.
doi:10.1515/forum.2010.051 fatcat:rhhmllnx45cefpef74u6aacpqm