Zobrazeno 1 - 10
of 317
pro vyhledávání: '"He, Xuhua"'
In this paper, we study the affine Deligne--Lusztig variety $X(\mu,b)_K$ and classify all quadruples $(\mathbf{G}, \mu, b, K)$ with $\dim X(\mu, b)_K=0$. This question was first asked by Rapoport in 2005, who also made an explicit conjecture in the h
Externí odkaz:
http://arxiv.org/abs/2402.15310
Autor:
Bao, Huanchen, He, Xuhua
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 Morse theory. In this paper, we construct explicitly acyclic complete ma
Externí odkaz:
http://arxiv.org/abs/2401.15933
We define the totally nonnegative matroid Schubert variety $\mathcal Y_V$ of a linear subspace $V \subset \mathbb R^n$. We show that $\mathcal Y_V$ is a regular CW complex homeomorphic to a closed ball, with strata indexed by pairs of acyclic flats o
Externí odkaz:
http://arxiv.org/abs/2310.18925
This paper presents a novel, interdisciplinary study that leverages a Machine Learning (ML) assisted framework to explore the geometry of affine Deligne-Lusztig varieties (ADLV). The primary objective is to investigate the nonemptiness pattern, dimen
Externí odkaz:
http://arxiv.org/abs/2308.11355
Autor:
He, Xuhua
Affine Lusztig varieties encode the orbital integrals of Iwahori-Hecke functions and serve as building blocks for the (conjectural) theory of affine character sheaves. In this paper, we establish a close relationship between affine Lusztig varieties
Externí odkaz:
http://arxiv.org/abs/2302.03203
Autor:
He, Xuhua
Motivated by Lusztig's $G$-stable pieces, we consider the combinatorial pieces: the pairs $(w, K)$ for elements $w$ in the Weyl group and subsets $K$ of simple reflections that are normalized by $w$. We generalize the notion of cyclic shift classes o
Externí odkaz:
http://arxiv.org/abs/2301.03264
Autor:
Bao, Huanchen, He, Xuhua
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 topological manifold with boundary. We also establish explicit parameterization
Externí odkaz:
http://arxiv.org/abs/2211.11168
In this paper, we study affine Deligne--Lusztig varieties $X_w(b)$ when the finite part of the element $w$ in the Iwahori--Weyl group is a partial $\sigma$-Coxeter element. We show that such $w$ is a cordial element and $X_w(b) \neq \emptyset$ if and
Externí odkaz:
http://arxiv.org/abs/2208.14058
Autor:
Bao, Huanchen, He, Xuhua
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) $J$-total positivity on the full flag variety of an arbitrary Kac-Moody group,
Externí odkaz:
http://arxiv.org/abs/2203.02137
Autor:
He, Xuhua, Lusztig, George
In this paper, we study the interaction between the totally positive monoid $G_{\ge 0}$ attached to a connected reductive group $G$ with a pinning and the conjugacy classes in $G$. In particular, we study how a conjugacy class meets the various cells
Externí odkaz:
http://arxiv.org/abs/2201.12479