Yongzhi Luan

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math.RT2026

Planar Convexity of Isotropy Orbits via Cohomology and Common Zeros

Yongzhi Luan, Tin-Yau Tam

Let $g$ be a noncompact simple real Lie algebra with a Cartan decomposition $g = k \oplus p$ . Let $K$ denote the connected Lie group corresp…

math.RT2026

A new proof for the partition algorithm of the annihilator varieties of highest weight modules

Zhanqiang Bai, Jing Jiang, Yongzhi Luan

Let $L (λ)$ be a simple highest weight module of a classical Lie algebra $g$ with highest weight $λ - ρ$ , where $ρ$ is half the sum of positive roots. Joseph proved that th…

math.RT2024

Dirac cohomology, branching laws and Wallach modules

Chao-Ping Dong, Yongzhi Luan, Haojun Xu

The idea of using Dirac cohomology to study branching laws was initiated by Huang, Pandzić and Zhu in 2013 [HPZ]. One of their results says that the Dirac cohomology of $π$ complet…

math.RT2024

Dirac series of $E_{8 (- 24)}$

Yi-Hao Ding, Chao-Ping Dong, Chengyu Du +2

This paper classifies the Dirac series of $E_{8 (- 24)}$ , the linear quaternionic real form of complex $E_{8}$ . One tool for us is a further sharpening of the Helgason-Johnson bound in…

Planar Convexity of Isotropy Orbits via Cohomology and Common Zeros

A new proof for the partition algorithm of the annihilator varieties of highest weight modules

Dirac cohomology, branching laws and Wallach modules

Dirac series of E8(−24)​

Dirac series of $E_{8 (- 24)}$