A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2008; you can also visit the original URL.
The file type is
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 indoi:10.1515/forum.2010.051 fatcat:rhhmllnx45cefpef74u6aacpqm