Simple Iwasawa modules with large canonical dimension of quaternion algebra over $\mathbb{Q}_p$
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915251499302912 |
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| author | Fu, Weibo |
| author_facet | Fu, Weibo |
| contents | We construct certain absolutely irreducible Banach representations of the quaternion algebra of large canonical (Gelfand-Kirillov) dimension which yield counterexamples to a natural conjecture of Dospinescu-Schraen on the existence of an infinitesimal character and topological finite length for the locally analytic vectors of an absolutely irreducible Banach representation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14490 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simple Iwasawa modules with large canonical dimension of quaternion algebra over $\mathbb{Q}_p$ Fu, Weibo Representation Theory Number Theory We construct certain absolutely irreducible Banach representations of the quaternion algebra of large canonical (Gelfand-Kirillov) dimension which yield counterexamples to a natural conjecture of Dospinescu-Schraen on the existence of an infinitesimal character and topological finite length for the locally analytic vectors of an absolutely irreducible Banach representation. |
| title | Simple Iwasawa modules with large canonical dimension of quaternion algebra over $\mathbb{Q}_p$ |
| topic | Representation Theory Number Theory |
| url | https://arxiv.org/abs/2504.14490 |