8 papers
Regularity of Totally Nonnegative Wonderful Compactification
Xuhua He, Kaitao Xie
Let 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…
Cohen-Macaulayness of Local Models via Shellability of the Admissible Set
Xuhua He, Felix Schremmer, Qingchao Yu
We prove that for any dominant cocharacter and any parahoric level , the augmented admissible set $\widehat{\Adm(μ)^K}$ in the Iwahori-Weyl group is dual EL-shellable. This…
Total positivity in twisted flag varieties
Xuhua He, Kaitao Xie
Let be a Kac-Moody group, split over . The totally nonnegative part of and its (ordinary) flag variety was introduced by Lusztig. It is known that the to…
Irreducible components of affine Lusztig varieties
Xuhua He
Let be a loop group and be its Iwahori-Weyl group. The affine Lusztig variety describes the intersection of the Bruhat cell $\mathcal{I} \dot{w} \ma…
Lusztig varieties for regular elements
Xuhua He, Ruben La
Let be a connected reductive group over an algebraically closed field. Let be a Borel subgroup of and be the associated Weyl group. We show that for any t…
Acyclic matchings on Bruhat intervals and applications to total positivity
Huanchen Bao, Xuhua He
The existence of acyclic complete matchings on the face poset of a regular CW complex implies that the underlying topological space of the CW complex is contractible by discrete Mo…
Total positivity for matroid Schubert varieties
Xuhua He, Connor Simpson, Kaitao Xie
We define the totally nonnegative matroid Schubert variety of a linear subspace . We show that is a regular CW complex homeomor…
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) -tota…