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Generalised Hermite constants, Voronoi theory and heights on flag varieties

Bertrand Meyer — 2009

Bulletin de la Société Mathématique de France

This paper explores the study of the general Hermite constant associated with 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 (, with Korkine–Zolotareff reduction), upper bounds and computation relative to these constants.

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