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Vertexwise criteria for admissibility of alcoves

Thomas J Haines Xuhua He

Representation Theory mathscidoc:1912.43206

American Journal of Mathematics, 139, (3), 769-784, 2017
We give a new description of the set {m 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.
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@inproceedings{thomas2017vertexwise,
  title={Vertexwise criteria for admissibility of alcoves},
  author={Thomas J Haines, and Xuhua He},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112934727676766},
  booktitle={American Journal of Mathematics},
  volume={139},
  number={3},
  pages={769-784},
  year={2017},
}
Thomas J Haines, and Xuhua He. Vertexwise criteria for admissibility of alcoves. 2017. Vol. 139. In American Journal of Mathematics. pp.769-784. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112934727676766.
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