Faces of highest weight modules and the universal Weyl polyhedron

@article{Dhillon2017FacesOH,
  title={Faces of highest weight modules and the universal Weyl polyhedron},
  author={Gurbir Singh Dhillon and Apoorva Khare},
  journal={Advances in Mathematics},
  year={2017},
  volume={319},
  pages={111-152}
}
Abstract Let V be a highest weight module over a Kac–Moody algebra g , and let conv V denote the convex hull of its weights. We determine the combinatorial isomorphism type of conv V, i.e. we completely classify the faces and their inclusions. In the special case where g is semisimple, this brings closure to a question studied by Cellini and Marietti (2015) [7] for the adjoint representation, and by Khare (2016, 2017) [17] , [18] for most modules. The determination of faces of finite… Expand

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