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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Neeb, Karl-Hermann / Noguchi, Junjiro / Shahidi, Freydoon / Sogge, Christopher D. / Wienhard, Anna

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Volume 22, Issue 5 (Jan 2010)

Issues

Kostant convexity for affine buildings

Petra Hitzelberger
Published Online: 2010-02-12 | DOI: https://doi.org/10.1515/forum.2010.051

Abstract

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 xA the set ρ(r –1(W .x)) is a certain convex hull of W .x. The proof can be reduced to a statement about Coxeter complexes and heavily relies on a character formula for highest weight representations of algebraic groups.

About the article

Received: 2008-03-12

Revised: 2009-03-02

Published Online: 2010-02-12

Published in Print: 2010-09-01



Citation Information: Forum Mathematicum, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum.2010.051. Export Citation

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[1]
Petra Hitzelberger
Advances in Mathematics, 2011, Volume 227, Number 1, Page 210

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