English

Reduction theory for stably graded Lie algebras

Number Theory 2025-01-22 v2 Representation Theory

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.

Keywords

Cite

@article{arxiv.2405.10217,
  title  = {Reduction theory for stably graded Lie algebras},
  author = {Jack A. Thorne},
  journal= {arXiv preprint arXiv:2405.10217},
  year   = {2025}
}

Comments

Accepted version