Kaitao Xie

activity

20232026

collaborators

4 papers

math.RT2026

Total positivity in twisted flag varieties

Xuhua He, Kaitao Xie

Let $G$ be a Kac-Moody group, split over $R$ . The totally nonnegative part of $G$ and its (ordinary) flag variety $G / B^{+}$ was introduced by Lusztig. It is known that the to…

math.RT2024

Theta Positivity in Lagrangian Grassmannian

Kaitao Xie

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 posit…

math.CO2023

Total positivity for matroid Schubert varieties

Xuhua He, Connor Simpson, Kaitao Xie

We define the totally nonnegative matroid Schubert variety $Y_{V}$ of a linear subspace $V \subset R^{n}$ . We show that $Y_{V}$ is a regular CW complex homeomor…

math.RT2023

Regularity of Unipotent Elements in Total Positivity

Haiyu Chen, Kaitao Xie

Let $G$ be a connected reductive group split over R. We show that every unipotent element in the totally nonnegative monoid of G is regular in some Levi subgroups, confirming a con…