Mathematics > Representation Theory
arXiv:2606.15401 (math)
[Submitted on 13 Jun 2026]
Abstract:Jensen, King, and Su described a category $\operatorname{CM}(C)$ which categorifies the cluster structure on the homogeneous coordinate ring of a Grassmannian. In this paper we describe subcategories $\operatorname{R}(v,w) \subseteq \operatorname{CM}(C)$ which lift Leclerc's categories $\mathcal{C}_{v,w}$ in the case where $v \in \left(W^{k}\backslash W\right)^{\max}$ and $w \geq v.$ As such, these categories are Frobenius, stably 2-CY, have natural cluster characters, and induce a cluster structure in lifts of open positroid varieties.
Submission history
From: Liam Riordan [view email]
[v1]
Sat, 13 Jun 2026 17:10:12 UTC (51 KB)
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