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arXiv · 2508.12171

The quasisymmetric flag variety: a toric complex on noncrossing partitions

Nantel Bergeron·Lucas Gagnon·Philippe Nadeau·Hunter Spink·Vasu Tewari
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Abstract

We develop the geometric theory of equivariant quasisymmetry via a new ``quasisymmetric flag variety''. This is a toric complex in the flag variety whose fixed point set is the set of noncrossing partitions, and whose cohomology ring is the ring of quasisymmetric coinvariants.

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Nantel Bergeron, Lucas Gagnon, Philippe Nadeau, Hunter Spink, Vasu Tewari. 2025-08-16. The quasisymmetric flag variety: a toric complex on noncrossing partitions. https://doi.org/10.1017/fmp.2026.10034

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