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A characterization of a special ordering in a root system.(English)Zbl 0799.20037

The author gives 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 \(R\) and characterizes the sets of positive roots which can be given such an ordering.

MSC:

20F55 Reflection and Coxeter groups (group-theoretic aspects)
17B20 Simple, semisimple, reductive (super)algebras

Cite

References:

[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). ·Zbl 0186.33001
[2]Howard Hiller, Geometry of Coxeter groups, Research Notes in Mathematics, vol. 54, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1982. ·Zbl 0483.57002
[3]James E. Humphreys, Introduction to Lie algebras and representation theory, Springer-Verlag, New York-Berlin, 1972. Graduate Texts in Mathematics, Vol. 9. ·Zbl 0254.17004
[4]James E. Humphreys, Reflection groups and Coxeter groups, Cambridge Studies in Advanced Mathematics, vol. 29, Cambridge University Press, Cambridge, 1990. ·Zbl 0725.20028
[5]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). ·Zbl 0135.07101
[6]George Lusztig, Quantum groups at roots of 1, Geom. Dedicata 35 (1990), no. 1-3, 89 – 113. ·Zbl 0714.17013 ·doi:10.1007/BF00147341
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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