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arXiv · 2404.03918

Dirac cohomology, branching laws and Wallach modules

Chao-Ping Dong·Yongzhi Luan·Haojun Xu
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Abstract

The idea of using Dirac cohomology to study branching laws was initiated by Huang, Pandzi\'c and Zhu in 2013 [HPZ]. One of their results says that the Dirac cohomology of $\pi$ completely determines $\pi|_{K}$, where $\pi$ is any irreducible unitarizable highest weight $(\mathfrak{g}, K)$ module. This paper aims to develop this idea for the exceptional Lie groups $E_{6(-14)}$ and $E_{7(-25)}$: we recover the $K$-spectrum of the Wallach modules from their Dirac cohomology.

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Chao-Ping Dong, Yongzhi Luan, Haojun Xu. 2024-04-05. Dirac cohomology, branching laws and Wallach modules. https://doi.org/10.1016/j.jalgebra.2024.10.022

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