Olha Shevchenko, UCLA

Title:  Rotationally symmetric plabic graphs and the Lagrangian Grassmannian

Abstract: The Totally Nonnegative Grassmannian $\rm{Gr}_{\geq 0} (k,n)$, introduced by Postnikov in 2006, is the subset of the real Grassmannian, consisting of  $k$-dimensional subspaces of $\mathbb{R}^n$ that can be represented by matrices with all nonnegative Plücker coordinates.
 
In this talk, we introduce the totally nonnegative Lagrangian Grassmannian $\rm{LG}^Q_{\geq 0} (n,2n)$,  a new subset of the totally nonnegative Grasmannian, determined by a specific bilinear form $Q$. We describe its cell structure, and show that each cell can be represented with a rotationally symmetric non-reduced plabic graph, which requires new machinery for non-reduced plabic graphs.