Generalised Hermite constants, Voronoi theory and heights on flag varieties

Bertrand Meyer

Bulletin de la Société Mathématique de France (2009)

  • Volume: 137, Issue: 1, page 127-158
  • ISSN: 0037-9484

Abstract

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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 (e.g., with Korkine–Zolotareff reduction), upper bounds and computation relative to these constants.

How to cite

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Meyer, Bertrand. "Generalised Hermite constants, Voronoi theory and heights on flag varieties." Bulletin de la Société Mathématique de France 137.1 (2009): 127-158. <http://eudml.org/doc/272326>.

@article{Meyer2009,
abstract = {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 (e.g., with Korkine–Zolotareff reduction), upper bounds and computation relative to these constants.},
author = {Meyer, Bertrand},
journal = {Bulletin de la Société Mathématique de France},
keywords = {lattices; Humbert forms; Hermite constant; Voronoï theory; flag variety; height},
language = {eng},
number = {1},
pages = {127-158},
publisher = {Société mathématique de France},
title = {Generalised Hermite constants, Voronoi theory and heights on flag varieties},
url = {http://eudml.org/doc/272326},
volume = {137},
year = {2009},
}

TY - JOUR
AU - Meyer, Bertrand
TI - Generalised Hermite constants, Voronoi theory and heights on flag varieties
JO - Bulletin de la Société Mathématique de France
PY - 2009
PB - Société mathématique de France
VL - 137
IS - 1
SP - 127
EP - 158
AB - 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 (e.g., with Korkine–Zolotareff reduction), upper bounds and computation relative to these constants.
LA - eng
KW - lattices; Humbert forms; Hermite constant; Voronoï theory; flag variety; height
UR - http://eudml.org/doc/272326
ER -

References

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