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Kostant convexity for affine buildings
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Petra Hitzelberger
Published/Copyright:
February 12, 2010
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 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 about Coxeter complexes and heavily relies on a character formula for highest weight representations of algebraic groups.
Received: 2008-03-12
Revised: 2009-03-02
Published Online: 2010-02-12
Published in Print: 2010-September
© de Gruyter 2010
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Articles in the same Issue
- Inhomogeneous Strichartz estimates
- Some characterizations of finite groups in which semipermutability is a transitive relation
- Fine gradings on the Lie algebra
- Harmonic analysis on a finite homogeneous space II: The Gelfand–Tsetlin decomposition
- Regularity results for the gradient of solutions of linear elliptic systems with VMO-coefficients and L1,λ data
- Amplitude inequalities for Differential Graded modules
- Homogeneous Lagrangian submanifolds of positive Euler characteristic
- Kostant convexity for affine buildings
- Algebraic monodromy and obstructions to formality
- Capacity and potentials on curves
- New characterizations of pseudo-coherent rings
- Le module de continuité des valeurs au bord des fonctions propres et des formes automorphes
