Xuhua He

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20222026

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5 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.RT2025

Irreducible components of affine Lusztig varieties

Xuhua He

Let $G ˘$ be a loop group and $W ~$ be its Iwahori-Weyl group. The affine Lusztig variety $Y_{w} (γ)$ describes the intersection of the Bruhat cell $\mathcal{I} \dot{w} \ma…

math.RT2025

Lusztig varieties for regular elements

Xuhua He, Ruben La

Let $G$ be a connected reductive group over an algebraically closed field. Let $B$ be a Borel subgroup of $G$ and $W$ be the associated Weyl group. We show that for any $w \in W$ t…

math.RT2022

Product structure and regularity theorem for totally nonnegative flag varieties

Huanchen Bao, Xuhua He

The totally nonnegative flag variety was introduced by Lusztig. It has enriched combinatorial, geometric, and Lie-theoretic structures. In this paper, we introduce a (new) $J$ -tota…