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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.08213 |
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Table of Contents:
- 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.