Rotationally symmetric plabic graphs and the Lagrangian Grassmannian
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914174073831424 |
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| author | Shevchenko, Olha |
| author_facet | Shevchenko, Olha |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_23446 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rotationally symmetric plabic graphs and the Lagrangian Grassmannian Shevchenko, Olha Combinatorics 14M15, 15B48 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. |
| title | Rotationally symmetric plabic graphs and the Lagrangian Grassmannian |
| topic | Combinatorics 14M15, 15B48 |
| url | https://arxiv.org/abs/2511.23446 |