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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.17422 |
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| _version_ | 1866910964226457600 |
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| author | Qin, Chuan |
| author_facet | Qin, Chuan |
| contents | Motivated by the recent work of Aubert-Xu and the techniques in G. Muic's article, we provide examples of computations of the Aubert-Zelevinsky duality functor for the principal and mediate series of the exceptional group $G_2$, and deduce corresponding results regarding the involution on the Hecke algebra side. These computations also allow us to confirm several instances of the Bernstein conjecture for $G_2$. This article is developed from part of the author's PhD thesis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17422 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Aubert-Zelevinsky involution for $G_2$ and its associated Hecke algebras Qin, Chuan Representation Theory Motivated by the recent work of Aubert-Xu and the techniques in G. Muic's article, we provide examples of computations of the Aubert-Zelevinsky duality functor for the principal and mediate series of the exceptional group $G_2$, and deduce corresponding results regarding the involution on the Hecke algebra side. These computations also allow us to confirm several instances of the Bernstein conjecture for $G_2$. This article is developed from part of the author's PhD thesis. |
| title | The Aubert-Zelevinsky involution for $G_2$ and its associated Hecke algebras |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2505.17422 |