Structure constants for simple Lie algebras from principal $\mathfrak{sl}_2$-triple
| Autor: | Abdesselam, Abdelmalek, Thomas, Alexander |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | For a simple complex Lie algebra $\mathfrak{g}$, fixing a principal $\mathfrak{sl}_2$-triple and highest weight vectors induces a basis of $\mathfrak{g}$ as vector space. For $\mathfrak{sl}_n$, we describe how to compute the Lie bracket in this basis using transvectants. This generalizes a well-known rule for $\mathfrak{sl}_2$ using Poisson brackets and degree 2 monomials in two variables. Our proof method uses a graphical calculus for classical invariant theory. Other Lie algebra types are discussed. Comment: 36 pages, 55 figures |
| Databáze: | arXiv |
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