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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.07652 |
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Table of 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.