Splicing positroid varieties

Abstract

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

13 pages