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arXiv · 2511.23446

Rotationally symmetric plabic graphs and the Lagrangian Grassmannian

Olha Shevchenko
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Abstract

We introduce the totally nonnegative Lagrangian Grassmannian $\rm{LG}_{\geq 0}^R (n,2n)$, a new subset of the totally nonnegative Grassmannian consisting of subspaces isotropic with respect to a certain bilinear form $R$. We describe its cell structure and show that each cell admits a representation by a rotationally symmetric (not necessarily reduced) plabic graph. Along the way, we develop new techniques for working with non-reduced plabic graphs.

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Olha Shevchenko. 2025-11-28. Rotationally symmetric plabic graphs and the Lagrangian Grassmannian. https://arxiv.org/abs/2511.23446

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