# MathSciDoc: An Archive for Mathematician ∫

#### Representation Theorymathscidoc: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 certainobtuse 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.
@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.