Canonical structure constants for simple Lie algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910406138658816 |
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| author | Geck, Meinolf Lang, Alexander |
| author_facet | Geck, Meinolf Lang, Alexander |
| contents | Let $\mathfrak{g}$ be a finite-dimensional simple Lie algebra over $\mathbb{C}$. In the 1950s Chevalley showed that $\mathfrak{g}$ admits particular bases, now called ``Chevalley bases'', for which the corresponding structure constants are integers. Such bases are not unique but, using Lusztig's theory of canonical bases, one can single out a ``canonical'' Chevalley basis which is unique up to a global sign. In this paper, we give explicit formulae for the structure constants with respect to such a basis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07652 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Canonical structure constants for simple Lie algebras Geck, Meinolf Lang, Alexander Representation Theory 20G40 Let $\mathfrak{g}$ be a finite-dimensional simple Lie algebra over $\mathbb{C}$. In the 1950s Chevalley showed that $\mathfrak{g}$ admits particular bases, now called ``Chevalley bases'', for which the corresponding structure constants are integers. Such bases are not unique but, using Lusztig's theory of canonical bases, one can single out a ``canonical'' Chevalley basis which is unique up to a global sign. In this paper, we give explicit formulae for the structure constants with respect to such a basis. |
| title | Canonical structure constants for simple Lie algebras |
| topic | Representation Theory 20G40 |
| url | https://arxiv.org/abs/2404.07652 |