Associated Representations of finite pattern groups
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915735369940992 |
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| author | Nien, Chufeng Wu, Chenyan |
| author_facet | Nien, Chufeng Wu, Chenyan |
| contents | In this paper, we consider the construction of irreducible representations of finite pattern groups in terms of Panov's associative polarization, which is a finite-field analogue of Kirillov's orbital method. Using this construction, first, we are able to classify the irreducible representations of the unipotent radical of the standard parabolic subgroups of $\mathrm{GL}_n$ with 4 parts; second, we can parameterize irreducible characters of degree $q$ in terms of coadjoint orbits of cardinality $q^2$, for any finite pattern groups $G$ over $\mathbb{F}_q,$ where $\mathbb{F}_q$ is a finite field with $q$ elements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11278 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Associated Representations of finite pattern groups Nien, Chufeng Wu, Chenyan Representation Theory In this paper, we consider the construction of irreducible representations of finite pattern groups in terms of Panov's associative polarization, which is a finite-field analogue of Kirillov's orbital method. Using this construction, first, we are able to classify the irreducible representations of the unipotent radical of the standard parabolic subgroups of $\mathrm{GL}_n$ with 4 parts; second, we can parameterize irreducible characters of degree $q$ in terms of coadjoint orbits of cardinality $q^2$, for any finite pattern groups $G$ over $\mathbb{F}_q,$ where $\mathbb{F}_q$ is a finite field with $q$ elements. |
| title | Associated Representations of finite pattern groups |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2601.11278 |