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Splicing positroid varieties
Algebraic Combinatorics, Volume 9 (2026) no. 2, pp. 577-594

We construct an explicit isomorphism between an open subset in the open positroid variety $\Pi _{k,n}^{\circ }$ in the Grassmannian $\mathrm{Gr}(k,n)$ and the product of two open positroid varieties $\Pi _{k,n-a+1}^{\circ }\times \Pi _{k,a+k-1}^{\circ }$. In the respective cluster structures, this isomorphism is given by freezing a certain subset of cluster variables and applying a cluster quasi-equivalence.

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Published online:
DOI: 10.5802/alco.478
Classification: 13F60, 14M15
Keywords: positroid varieties, cluster algebras
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
Gorsky, Eugene; Scroggin, Tonie. Splicing positroid varieties. Algebraic Combinatorics, Volume 9 (2026) no. 2, pp. 577-594. doi: 10.5802/alco.478
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