Generalised Hermite Constants, Voronoi Theory and Heights on Flag Varieties

Bertrand Meyer (1)

1 IMB - Institut de Mathématiques de Bordeaux

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.

Mots clés: Hermite constant; Voronoi theory

Domaines: Théorie des nombres [math.NT]

Bertrand Meyer. Generalised Hermite Constants, Voronoi Theory and Heights on Flag Varieties. Bulletin de la société mathématique de France, 2009, 137 (1), p 127-158. ⟨hal-00268899⟩