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Spherical Schubert varieties in GLn / P

  • Jaewon Min
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Abstract

Let a general linear group act on a partial flag variety transitively, and consider the induced action of a Levi subgroup L. A Schubert variety is L−spherical if it is stable under the L-action and contains a dense open orbit of a Borel subgroup of L. It is toric if, in addition, L is a torus. In this paper, we give a combinatorial classification of L-spherical Schubert varieties in partial flag varieties. This is achieved by applying Lakshmibai-Seshadri paths forming crystal graphs of Demazure modules. Previously, 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. Our classification generalizes and unifies these results.

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Cite

BibTeXRIS
BibTeX
@misc{min2026spherical,
  title = {{Spherical Schubert varieties in $GL_n / P$}},
  author = {Jaewon Min},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00321},
  eprint = {2611.00321},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00321},
}
RIS
TY  - UNPB
TI  - Spherical Schubert varieties in GL_n / P
AU  - Jaewon Min
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00321
UR  - https://arxiv.org/abs/2611.00321
AB  - Let a general linear group act on a partial flag variety transitively, and consider the induced action of a Levi subgroup L. A Schubert variety is L−spherical if it is stable under the L-action and contains a dense open orbit of a Borel subgroup of L. It is toric if, in addition, L is a torus. In this paper, we give a combinatorial classification of L-spherical Schubert varieties in partial flag varieties. This is achieved by applying Lakshmibai-Seshadri paths forming crystal graphs of Demazure modules. Previously, 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. Our classification generalizes and unifies these results.
ER  -