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arXiv · 2405.10217

Reduction theory for stably graded Lie algebras

Jack A. Thorne
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Abstract

We define a reduction covariant for the representations a la Vinberg associated to stably graded Lie algebras. We then give an analogue of the LLL algorithm for the odd split special orthogonal group and show how this can be combined with our theory to effectively reduce the coefficients of vectors in a representation connected to 2-descent for odd hyperelliptic curves.

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Jack A. Thorne. 2024-05-16. Reduction theory for stably graded Lie algebras. https://arxiv.org/abs/2405.10217

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