# Coxeter combinatorics and spherical Schubert geometry

@article{Hodges2020CoxeterCA, title={Coxeter combinatorics and spherical Schubert geometry}, author={Reuven Hodges and Alexander Yong}, journal={arXiv: Representation Theory}, year={2020} }

For a finite Coxeter system and a subset of its diagram nodes, we define spherical elements (a generalization of Coxeter elements). Conjecturally, for Weyl groups, spherical elements index Schubert varieties in a flag manifold G/B that are spherical for the action of a Levi subgroup. We evidence the conjecture, employing the combinatorics of Demazure modules, and work of R. Avdeev-A. Petukhov, M. Can-R. Hodges, R. Hodges-V. Lakshmibai, P. Karuppuchamy, P. Magyar-J. Weyman-A. Zelevinsky, N… Expand

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