Classification of Certain Regular Subalgebras of $\mathfrak{sl}(n, \mathbb C)$ up to Conjugacy
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911933325639680 |
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| author | Dhar, Shreya |
| author_facet | Dhar, Shreya |
| contents | In this paper we will be classifying some regular upper-triangular subalgebras of $\mathfrak{sl}(n, \mathbb C)$ up to conjugacy by matrices in $SL(n, \mathbb C)$. We do so for dimension 2, codimension 1, and codimension 2 subalgebras. We prove some general results for codimension $k$. The approach we use reduces an abstract classification problem to a combinatorial one, which we solve through a mixture of inductive and computational approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17833 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classification of Certain Regular Subalgebras of $\mathfrak{sl}(n, \mathbb C)$ up to Conjugacy Dhar, Shreya Representation Theory In this paper we will be classifying some regular upper-triangular subalgebras of $\mathfrak{sl}(n, \mathbb C)$ up to conjugacy by matrices in $SL(n, \mathbb C)$. We do so for dimension 2, codimension 1, and codimension 2 subalgebras. We prove some general results for codimension $k$. The approach we use reduces an abstract classification problem to a combinatorial one, which we solve through a mixture of inductive and computational approaches. |
| title | Classification of Certain Regular Subalgebras of $\mathfrak{sl}(n, \mathbb C)$ up to Conjugacy |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2406.17833 |