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arXiv · 1109.0336

GL(p) x GL(q)-orbit closures on the flag variety and Schubert structure constants for (p,q)-pairs

Benjamin J. Wyser
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Abstract

We give positive combinatorial descriptions of Schubert structure constants $c_{u,v}^w$ for the full flag variety in type $A_{n-1}$ when $u$ and $v$ form what we refer to as a "$(p,q)$-pair" ($p+q=n$). The key observation is that a certain subset of the $GL(p,\mathbb{C}) \times GL(q,\mathbb{C})$-orbit closures on the flag variety (those satisfying an easily stated pattern avoidance condition) are Richardson varieties. The result on structure constants follows when one combines this observation with a theorem of Brion concerning intersection numbers of spherical subgroup orbit closures and Schubert varieties.

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Benjamin J. Wyser. 2011-09-02. GL(p) x GL(q)-orbit closures on the flag variety and Schubert structure constants for (p,q)-pairs. https://arxiv.org/abs/1109.0336

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