Splicing positroid varieties

Eugene Gorsky; Tonie Scroggin

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arXiv · 2405.15112

Splicing positroid varieties

Eugene Gorsky·Tonie Scroggin

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Abstract

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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Eugene Gorsky, Tonie Scroggin. 2024-05-24. Splicing positroid varieties. https://arxiv.org/abs/2405.15112

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