Generalised Hermite Constants, Voronoi Theory and Heights on Flag Varieties
Number Theory
2008-12-18 v1
Abstract
This paper explores the study of the general Hermite constant associated to the general linear group and its irreducible representations, as defined by T. Watanabe. To that end, a height, which naturally applies to flag varieties, is built and notions of perfection and eutaxy characterising extremality are introduced. Finally we acquaint some relations (e.g. with Korkine--Zolotareff reduction), upper bounds and computation relative to these constants.
Keywords
Cite
@article{arxiv.0804.0292,
title = {Generalised Hermite Constants, Voronoi Theory and Heights on Flag Varieties},
author = {Bertrand Meyer},
journal= {arXiv preprint arXiv:0804.0292},
year = {2008}
}