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arXiv · 2309.01747

The HHMP decomposition of the permutohedron and degenerations of torus orbits in flag varieties

Carl Lian
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Abstract

Let $Z\subset Fl(n)$ be the closure of a generic torus orbit in the full flag variety. Anderson-Tymoczko express the cohomology class of $Z$ as a sum of classes of Richardson varieties. Harada-Horiguchi-Masuda-Park give a decomposition of the permutohedron, the moment map image of $Z$, into subpolytopes corresponding to the summands of the Anderson-Tymoczko formula. We construct an explicit toric degeneration inside $Fl(n)$ of $Z$ into Richardson varieties, whose moment map images coincide with the HHMP decomposition, thereby obtaining a new proof of the Anderson-Tymoczko formula.

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Carl Lian. 2023-09-04. The HHMP decomposition of the permutohedron and degenerations of torus orbits in flag varieties. https://arxiv.org/abs/2309.01747

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