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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2602.19632 |
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| _version_ | 1866914344010252288 |
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| author | Geck, Meinolf |
| author_facet | Geck, Meinolf |
| contents | Let $\mathfrak{g}$ be a simple Lie algebra over~$\mathbb{C}$ with root system~$Φ$. In the simply laced case, Frenkel and Kac found a particularly simple construction of~$\mathfrak{g}$, together with a Chevalley basis and explicitly given structure constants, in terms of a certain multiplicative $2$-cocycle $\varepsilon\colon \mathbb{Z} Φ\times \mathbb{Z}Φ\rightarrow\{\pm 1\}$. We show that Lusztig's canonical basis of~$\mathfrak{g}$ can also be obtained in this way, for a suitable choice of~$\varepsilon$. We also address the problem of explicitly describing the structure constants when $Φ$ is not simply laced. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19632 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Lusztig's canonical bases of simple Lie algebras Geck, Meinolf Representation Theory 20G40, 17B45 Let $\mathfrak{g}$ be a simple Lie algebra over~$\mathbb{C}$ with root system~$Φ$. In the simply laced case, Frenkel and Kac found a particularly simple construction of~$\mathfrak{g}$, together with a Chevalley basis and explicitly given structure constants, in terms of a certain multiplicative $2$-cocycle $\varepsilon\colon \mathbb{Z} Φ\times \mathbb{Z}Φ\rightarrow\{\pm 1\}$. We show that Lusztig's canonical basis of~$\mathfrak{g}$ can also be obtained in this way, for a suitable choice of~$\varepsilon$. We also address the problem of explicitly describing the structure constants when $Φ$ is not simply laced. |
| title | On Lusztig's canonical bases of simple Lie algebras |
| topic | Representation Theory 20G40, 17B45 |
| url | https://arxiv.org/abs/2602.19632 |