Theta Positivity in Lagrangian Grassmannian

2024/08/05 by K. J. Xie, Xie, Kaitao · 1 citation
Mathematics · Physics and Astronomy · #14M15 #15B48 #20G20 #Advanced Differential Geometry Research #Advanced Mathematical Theories and Applications #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2408.02607

openalex publication_date 2024/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the theta nonnegative part of Lagrangian Grassmannian. We show that it admits an orbital decomposition and is homeomorphic to a closed ball. We compare it with other positive structures. We show that it contains several totally nonnegative parts of Lagrangian Grassmannian subject to certain choices of pinnings and agrees with the nonnegativity of the generalized Plücker coordinates.

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• Positivity and Non-commutativity

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