Kaitao Xie

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20232026

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4 papers · 1 filter

math.RT2026

Regularity of Totally Nonnegative Wonderful Compactification

Xuhua He, Kaitao Xie

Let $G$ be a split real semisimple group of adjoint type. We prove that the cellular decomposition of the totally nonnegative part of its wonderful compactification is a regular CW…

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.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…