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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The stretched weight lattices of a Weyl group


Author: Daniel R. Farkas
Journal: Proc. Amer. Math. Soc. 92 (1984), 473-477
MSC: Primary 17B10; Secondary 17B20
MathSciNet review: 760928
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Abstract: Consider a finite group of automorphisms of a lattice. The nonnegative cone is a fundamental domain (for the action of the group on the lattice) if and only if the group is a Weyl group and the lattice is isomorphic, as a module, to one of the group's stretched weight lattices.


References [Enhancements On Off] (What's this?)

  • [1] N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles, No. 1337, Hermann, Paris, 1968 (French). MR 0240238 (39 #1590)
  • [2] Daniel R. Farkas, Multiplicative invariants, Enseign. Math. (2) 30 (1984), no. 1-2, 141–157. MR 743674 (85h:16042)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0760928-0
PII: S 0002-9939(1984)0760928-0
Keywords: Weyl group, weight lattice, fundamental domain
Article copyright: © Copyright 1984 American Mathematical Society