On the Mathieu Conjecture for $Sp(N)$ and $G_2$
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909560865816576 |
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| author | Zwart, Kevin |
| author_facet | Zwart, Kevin |
| contents | As a direct continuation of K. Zwart, arXiv:2304.02648, which is built on the work of M. Müger and L. Tuset, we reduce the Mathieu conjecture, formulated by O. Mathieu in 1997, for $Sp(N)$ and $G_2$ to a conjecture involving functions over $\mathbb{R}^n\times (S^1)^m$ with $n,m\in\mathbb{N}_0$. The proofs rely on Euler-style parametrizations of these groups, a specific version of the $KAK$ decomposition, which we discuss and prove. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02813 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Mathieu Conjecture for $Sp(N)$ and $G_2$ Zwart, Kevin Group Theory 22E30, 43A75 As a direct continuation of K. Zwart, arXiv:2304.02648, which is built on the work of M. Müger and L. Tuset, we reduce the Mathieu conjecture, formulated by O. Mathieu in 1997, for $Sp(N)$ and $G_2$ to a conjecture involving functions over $\mathbb{R}^n\times (S^1)^m$ with $n,m\in\mathbb{N}_0$. The proofs rely on Euler-style parametrizations of these groups, a specific version of the $KAK$ decomposition, which we discuss and prove. |
| title | On the Mathieu Conjecture for $Sp(N)$ and $G_2$ |
| topic | Group Theory 22E30, 43A75 |
| url | https://arxiv.org/abs/2403.02813 |