Skip Navigation


Bulletin of the London Mathematical Society Advance Access originally published online on February 24, 2009
Bulletin of the London Mathematical Society 2009 41(2):227-241; doi:10.1112/blms/bdn120
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
41/2/227    most recent
bdn120v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Montagard, P.-L.
Right arrow Articles by Ressayre, N.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2009 London Mathematical Society

Regular lattice polytopes and root systems

Pierre-Louis Montagard and Nicolas Ressayre

Institut de Mathématiques et Modélisation de Montpellier
Université Montpellier 2
UMR CNRS 5149
Case Courrier 051
Place Eugène Bataillon
34095 Montpellier cedex
France
montagar@math.univ-montp2.fr

Received 15 June 2007. Revision received 1 October 2008.

Consider {Lambda}, a lattice in a real finite-dimensional vector space. Here we are interested in lattice polytopes, that is, convex polytopes with vertices in {Lambda}. Consider the group G of the affine real transformations that map the lattice onto itself. Replacing the group of Euclidean motions by the group G one can define the notion of regular lattice polytopes. More precisely, a lattice polytope is said to be regular if the subgroup of G which preserves the polytope acts transitively on the set of its complete flags. In this paper, we associate to each regular lattice polytope a root system. This association allows us to give a new proof of the classification of regular lattice polytopes recently obtained by Karpenkov.

2000 Mathematics Subject Classification 52B20 (primary), 52B15, 51F15 (secondary).


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.