On flips of unitary buildings I: Classification of flips

Structure of Hyperbolic Unitary Groups II: Classification of E-normal Subgroups

This paper proves the sandwich classification conjecture for subgroups of an even dimensional hyperbolic unitary group $U_{2n}(R,Λ)$ which are normalized by the elementary subgroup $EU_{2n}(R,Λ)$, under the condition that $R$ is a quasi-finite ring with involution, i.e a direct limit of module finite rings with involution, and $n\geq 3$.

Classification of Sylow classes of parabolic and reflection subgroups in unitary reflection groups

Let $\ell$ be a prime divisor of the order of a finite unitary reflection group. We classify up to conjugacy the parabolic and reflection subgroups that are minimal with respect to inclusion, subject to containing an $\ell$-Sylow subgroup. The classification assists in describing the $\ell$-Sylow subgroups of unitary reflection groups up to group isomorphism. This classification also relates to the modular representation theory of finite groups of Lie type. We observe that unless a parabolic subgroup minimally containing an $\ell$-Sylow subgroup is $G$ itself, the reflection subgroup within th…

广义特殊酉代数$\mathfrak{su}(2,1)$的子代数

The subalgebras of the generalized special unitary algebra $\mathfrak{su}(2,1)$

本研究结合伽罗瓦上同调与已有复子代数分类结果，完成了广义特殊酉代数$\mathfrak{su}(2,1)$的实子代数分类，填补了$\mathfrak{sl}_3(\mathbb{C})$非紧实形式实子代数分类的剩余空白。

通过根嵌入和$θ$-投影对E6(-14)的酉表示分类：一种基于Sp(4)的秩2约化框架

Classification of Unitary Representations for E6(-14) via Root Embedding and $θ$-Projection: A Rank-2 Reduction Framework with Sp(4)

针对例外李群E6非紧实形式E6(-14)酉表示分类的计算瓶颈，本文提出整合根嵌入、$θ$-投影与朗兰兹参数化的秩2约化框架，将问题从6维降至2维，证明表示对应单射性与类型保持性，为其提供算法化分类工具并可推广至更高秩例外群。