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| Format: | Preprint |
| Veröffentlicht: |
2023
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| Online-Zugang: | https://arxiv.org/abs/2312.02794 |
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| _version_ | 1866911762817744896 |
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| author | Yang, Jae-Hyun |
| author_facet | Yang, Jae-Hyun |
| contents | In this paper, we introduce the notion of automorphic forms for $GL(n,\BZ)\ltimes \BZ^{(m,n)}$ and discuss invariant differential operators on the Minkowski-Euclid space. The group $GL{n,\BR}\ltimes \BR^{(m,n)}$ is the semidirect product of $GL(n,\BR)$ and the additive group $\BR^{(m,n)}$ and is {\it not} a reductive group. The Minkowski-Euclid space is the quotient space of $GL(n,\BR)\ltimes \BR^{(m,n)}$ by $O(n,\BR)$. The Minkowski-Euclid space is an important non-symmetric homogeneous space geometrically and number theoretically. We present some open problems to be solved in the future. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_02794 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Introduction to Automorphic Forms for $GL(n,\BZ)\ltimes \BZ^{(m,n)}$ Yang, Jae-Hyun Number Theory In this paper, we introduce the notion of automorphic forms for $GL(n,\BZ)\ltimes \BZ^{(m,n)}$ and discuss invariant differential operators on the Minkowski-Euclid space. The group $GL{n,\BR}\ltimes \BR^{(m,n)}$ is the semidirect product of $GL(n,\BR)$ and the additive group $\BR^{(m,n)}$ and is {\it not} a reductive group. The Minkowski-Euclid space is the quotient space of $GL(n,\BR)\ltimes \BR^{(m,n)}$ by $O(n,\BR)$. The Minkowski-Euclid space is an important non-symmetric homogeneous space geometrically and number theoretically. We present some open problems to be solved in the future. |
| title | Introduction to Automorphic Forms for $GL(n,\BZ)\ltimes \BZ^{(m,n)}$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2312.02794 |