Séminaire Lotharingien de Combinatoire, 95B.98 (2026), 12 pp.
Jaewon Min
When is a Schubert Variety Spherical?
Abstract.
Let L be a Levi subgroup of a general linear group acting on a Schubert variety. If there is a dense open orbit of a Borel subgroup, the Schubert variety is L-spherical, generalizing the concept of toric varieties. Hodges and Lakshmibai classified L-spherical Schubert varieties in Grassmannians. L-spherical Schubert varieties in complete flag varieties were treated independently by Gao-Hodges-Yong and Can-Saha. In this paper, we generalize these classifications to Schubert varieties in partial flag varieties of type A. This is achieved by applying Lakshmibai-Seshadri paths forming crystal graphs of Demazure modules, which has a root-system uniform framework.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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