Dirac series of $\mathrm{GL}(n)$ over an Archimedean field
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866915358919622656 |
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| author | Ding, Yihao Zhang, Hongfeng |
| author_facet | Ding, Yihao Zhang, Hongfeng |
| contents | Motivated by the $(\mathfrak{g},K)$-cohomology and Dirac cohomology, we determine Dirac series of $\mathrm{GL}(n,\mathbb{H})$, and show that the spin lowest $K$-type of any Dirac series, which determines the Dirac cohomology, is unique and multiplicity-free for both $\mathrm{GL}(n,\mathbb{H})$ and $\mathrm{GL}(n,\mathbb{R})$. This verifies a conjecture about uniqueness of the spin lowest $K$-type of Dirac series for $\mathrm{GL}(n,\mathbb{R})$ proposed by Dong and Wong. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_09903 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Dirac series of $\mathrm{GL}(n)$ over an Archimedean field Ding, Yihao Zhang, Hongfeng Representation Theory 22E46 Motivated by the $(\mathfrak{g},K)$-cohomology and Dirac cohomology, we determine Dirac series of $\mathrm{GL}(n,\mathbb{H})$, and show that the spin lowest $K$-type of any Dirac series, which determines the Dirac cohomology, is unique and multiplicity-free for both $\mathrm{GL}(n,\mathbb{H})$ and $\mathrm{GL}(n,\mathbb{R})$. This verifies a conjecture about uniqueness of the spin lowest $K$-type of Dirac series for $\mathrm{GL}(n,\mathbb{R})$ proposed by Dong and Wong. |
| title | Dirac series of $\mathrm{GL}(n)$ over an Archimedean field |
| topic | Representation Theory 22E46 |
| url | https://arxiv.org/abs/2208.09903 |