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arXiv · 2604.24903

The Quasisymmetric Grassmannian

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

We construct a complex of toric varieties we call the quasisymmetric Grassmannian inside the Grassmannian of $r$-planes in $\mathbb{C}^n$. Each irreducible component is a positroid variety and an $S_n$ translate of a toric Richardson variety of ribbon shape. We describe it as the vanishing locus of equations $\Delta_A\Delta_{A'}=0$ in Pl\"ucker coordinates determined by a new noncrossing combinatorial object we call the quasisymmetric Johnson graph. We give an affine paving, and show that its cohomology ring is a quasisymmetric modification of the Borel presentation of the Grassmannian's cohomology, with fundamental quasisymmetric polynomials playing the role of Schur polynomials.

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Nantel Bergeron, Lucas Gagnon, Hunter Spink, Vasu Tewari. 2026-04-27. The Quasisymmetric Grassmannian. https://arxiv.org/abs/2604.24903

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