Abstract: Over the last several years, in joint work with V. Lakshmibai and M. B. Can, I have been studying Levi subgroup actions on Schubert varieties. In particular, we are interested in when a Schubert variety is a spherical variety for the action of a Levi subgroup. Recently, we gave a classification of the Schubert varieties in the Grassmannian that are Levi spherical. I will discuss this classification as well as work in progress with A. Yong on extending the classification to Schubert varieties in the full flag variety.
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