Generalised Hermite Constants, Voronoi Theory and Heights on Flag Varieties

Details Generalised Hermite Constants, Voronoi Theory and Heights on Flag Varieties Generalised Hermite Constants, Voronoi Theory and Heights on Flag Varieties

2008-04-02

arxiv.org/abs/0804.0292v1

Mathematics

Number Theory

Scientific paper

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.

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