Xuhua He

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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 $Y_{w} (I^^{3})$ describes the intersection of the Bruhat cell $\mathcal{I} \dot{w} \m…

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…