Mathematics Colloquia and Seminars

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A Schubert variety in the complete flag variety GL_n/B is Levi-spherical if the action of a Borel subgroup in a Levi subgroup of a standard parabolic subgroup has an open dense orbit. I will present some recent work, joint with Alexander Yong and Yibo Gao, giving a classification of Levi-spherical Schubert varieties in terms of spherical elements of a symmetric group. To achieve this, we establish connections with the key polynomials of Lascoux-Schutzenberger, multiplicity-freeness, and split-symmetry in algebraic combinatorics.