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Vertexwise criteria for admissibility of alcoves
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 139, Number 3, June 2017
- pp. 769-784
- 10.1353/ajm.2017.0020
- Article
- Additional Information
We give a new description of the set ${\rm Adm}(\mu)$ of admissible alcoves as an intersection of certain ``obtuse cones'' of alcoves, and we show this description may be given by imposing conditions vertexwise. We use this to prove the vertexwise admissibility conjecture of Pappas-Rapoport-Smithling. The same idea gives simple proofs of two ingredients used in the proof of the Kottwitz-Rapoport conjecture on existence of crystals with additional structure.