Cohen Macaulay modules and positroid varieties

Abstract

Jensen, King, and Su described a category $\mathrm{CM}(C)$ which categorifies the cluster structure on the homogeneous coordinate ring of a Grassmannian. In this paper we describe subcategories $R(v,w)\subseteq \mathrm{CM}(C)$ which lift Leclerc's categories ${\mathcal{C}}_{v,w}$ in the case where $v\in {\left(W^k\backslash W\right)}^{\max }$ and $w\ge v.$ As such, these categories are Frobenius, stably 2-CY, have natural cluster characters, and induce a cluster structure in lifts of open positroid varieties.

61 pages. Part of the author's PhD thesis