ICTS:30027

Video URL

Plucker inequalities for weakly separated coordinates in the TNN Grassmannian

Plucker inequalities for weakly separated coordinates in the TNN Grassmannian

(2024). Plucker inequalities for weakly separated coordinates in the TNN Grassmannian. SciVideos. https://youtube.com/live/vmj5ZIOAHjE

Plucker inequalities for weakly separated coordinates in the TNN Grassmannian. SciVideos, Oct. 22, 2024, https://youtube.com/live/vmj5ZIOAHjE 

          @misc{ scivideos_ICTS:30027,
            doi = {},
            url = {https://youtube.com/live/vmj5ZIOAHjE},
            author = {},
            keywords = {},
            language = {en},
            title = {Plucker inequalities for weakly separated coordinates in the TNN Grassmannian},
            publisher = {},
            year = {2024},
            month = {oct},
            note = {ICTS:30027 see, \url{https://scivideos.org/icts-tifr/30027}}
          }
Prateek Kumar Vishwakarma
Talk numberICTS:30027
Source RepositoryICTS-TIFR
Source EventDiscrete integrable systems: difference equations, cluster algebras and probabi…
Collection

Abstract

We show that the partial sums of the long Plucker relations for pairs of weakly separated Plucker coordinates oscillate around 0 on the totally nonnegative part of the Grassmannian. Our result generalizes the classical oscillating inequalities by Gantmacher–Krein (1941) and recent results on totally nonnegative matrix inequalities by Fallat–Vishwakarma (2023). In fact we obtain a characterization of weak separability, by showing that no other pair of Plucker coordinates satisfies this property. Weakly separated sets were initially introduced by Leclerc and Zelevinsky and are closely connected with the cluster algebra of the Grassmannian. Moreover, our work connects several fundamental objects such as weak separability, Temperley–Lieb immanants, and Plucker relations, and provides a very general and natural class of additive determinantal inequalities on the totally nonnegative part of the Grassmannian. This is joint work with Soskin.