A characterization of a special ordering in a root system
HTML articles powered by AMS MathViewer
- by Paolo Papi
- Proc. Amer. Math. Soc. 120 (1994), 661-665
- DOI: https://doi.org/10.1090/S0002-9939-1994-1169886-7
- PDF | Request permission
Abstract:
We give necessary and sufficient conditions for an ordering of a set of positive roots in a root system $R$ to be associated to a reduced expression of an element of the Weyl group of $R$. Finally we characterize the sets of positive roots which can be given such an ordering.References
- 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 [Current Scientific and Industrial Topics], No. 1337, Hermann, Paris, 1968 (French). MR 0240238
- Howard Hiller, Geometry of Coxeter groups, Research Notes in Mathematics, vol. 54, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1982. MR 649068
- James E. Humphreys, Introduction to Lie algebras and representation theory, Graduate Texts in Mathematics, Vol. 9, Springer-Verlag, New York-Berlin, 1972. MR 0323842
- James E. Humphreys, Reflection groups and Coxeter groups, Cambridge Studies in Advanced Mathematics, vol. 29, Cambridge University Press, Cambridge, 1990. MR 1066460, DOI 10.1017/CBO9780511623646
- Nagayoshi Iwahori, On the structure of a Hecke ring of a Chevalley group over a finite field, J. Fac. Sci. Univ. Tokyo Sect. I 10 (1964), 215–236 (1964). MR 165016
- George Lusztig, Quantum groups at roots of $1$, Geom. Dedicata 35 (1990), no. 1-3, 89–113. MR 1066560, DOI 10.1007/BF00147341
Bibliographic Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 661-665
- MSC: Primary 20F55
- DOI: https://doi.org/10.1090/S0002-9939-1994-1169886-7
- MathSciNet review: 1169886