Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.03918 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909378629599232 |
|---|---|
| author | Dong, Chao-Ping Luan, Yongzhi Xu, Haojun |
| author_facet | Dong, Chao-Ping Luan, Yongzhi Xu, Haojun |
| contents | 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 $π$ completely determines $π|_{K}$, where $π$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03918 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dirac cohomology, branching laws and Wallach modules Dong, Chao-Ping Luan, Yongzhi Xu, Haojun Representation Theory 22E46 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 $π$ completely determines $π|_{K}$, where $π$ 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. |
| title | Dirac cohomology, branching laws and Wallach modules |
| topic | Representation Theory 22E46 |
| url | https://arxiv.org/abs/2404.03918 |