An addendum on the Mathieu Conjecture for $SU(N)$, $Sp(N)$ and $G_2$
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912344668372992 |
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| author | Zwart, Kevin |
| author_facet | Zwart, Kevin |
| contents | In this paper, we sharpen results obtained by the author in 2023. The new results reduce the Mathieu Conjecture on $SU(N)$ (formulated for all compact connected Lie groups by O. Mathieu in 1997) to a conjecture involving only functions on $\mathbb{R}^n\times (S^1)^m$ with $n,m$ non-negative integers instead of involving functions on $\mathbb{R}^n\times (S^1\setminus\{1\})^m$. The proofs rely on a more recent work of the author (2024) and a specific $KAK$ decomposition. Finally, with these results we can also improve the results on the groups $Sp(N)$ and $G_2$ in the latter paper, since they relied on the construction introduced in the 2023 paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01516 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An addendum on the Mathieu Conjecture for $SU(N)$, $Sp(N)$ and $G_2$ Zwart, Kevin Group Theory 22E30, 43A75 In this paper, we sharpen results obtained by the author in 2023. The new results reduce the Mathieu Conjecture on $SU(N)$ (formulated for all compact connected Lie groups by O. Mathieu in 1997) to a conjecture involving only functions on $\mathbb{R}^n\times (S^1)^m$ with $n,m$ non-negative integers instead of involving functions on $\mathbb{R}^n\times (S^1\setminus\{1\})^m$. The proofs rely on a more recent work of the author (2024) and a specific $KAK$ decomposition. Finally, with these results we can also improve the results on the groups $Sp(N)$ and $G_2$ in the latter paper, since they relied on the construction introduced in the 2023 paper. |
| title | An addendum on the Mathieu Conjecture for $SU(N)$, $Sp(N)$ and $G_2$ |
| topic | Group Theory 22E30, 43A75 |
| url | https://arxiv.org/abs/2504.01516 |