63 citations · 308 across the 74 of their papers we have counts for
48 papers · 1 filter
On affine Lusztig varieties
Xuhua He
Affine Lusztig varieties encode the orbital integrals of Iwahori--Hecke functions and serve as building blocks for the (conjectural) theory of affine character sheaves. We establis…
A generalization of cyclic shift classes
Xuhua He
Motivated by Lusztig's -stable pieces, we consider the combinatorial pieces: the pairs for elements in the Weyl group and subsets of simple reflections that are…
Total positivity in twisted product of flag varieties
Huanchen Bao, Xuhua He
We show that the totally nonnegative part of the twisted product of flag varieties of a Kac-Moody group admits a cellular decomposition, and the closure of each cell is a topologic…
Affine Deligne--Lusztig varieties with finite Coxeter parts
Xuhua He, Sian Nie, Qingchao Yu
In this paper, we study affine Deligne--Lusztig varieties when the finite part of the element in the Iwahori--Weyl group is a partial -Coxeter element. We show that…
Total positivity and conjugacy classes
Xuhua He, George Lusztig
In this paper, we study the interaction between the totally positive monoid attached to a connected reductive group with a pinning and the conjugacy classes in .…
Demazure product of the affine Weyl groups
Xuhua He, Sian Nie
The Demazure product gives a natural monoid structure on any Coxeter group. Such structure occurs naturally in many different areas in Lie Theory. This paper studies the Demazure p…