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Conjugacy classes of involutions in Coxeter groups

Published online by Cambridge University Press:  17 April 2009

R.W. Richardson
R.W. Richardson
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, PO Box 4, Canberra, ACT 2600, Australia.
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Abstract

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In this paper we give an elementary method for classifying conjugacy classes of involutions in a Coxeter group (W, S). The classification is in terms of (W-equivalence classes of certain subsets of S).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 26 , Issue 1 , August 1982 , pp. 1 - 15
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Bala, P. and Carter, R.W., “Classes of unipotent elements in simple algebraic groups. II”, Math. Proc. Cambridge Philos. Soc. 80 (1976), 1–18.CrossRefGoogle Scholar
[2]Bourbaki, N., Éléements 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, 1337. Hermann, Paris, 1968).Google Scholar
[3]Carter, R.W., “Conjugacy classes in the Weyl group”, Compositio Math. 25 (1972), 1–59.Google Scholar
[4]Deodhar, Vinay V., “On the root system of a Coxeter group”, Comm. Algebra 10 (1982), 611–630.CrossRefGoogle Scholar
[5]Howlett, Robert B., “Normalizers of parabolic subgroups of reflection groups”, J. London Math. Soc. (2) 21 (1980), 62–80.CrossRefGoogle Scholar
[6]Steinberg, Robert, Endomorphisms of linear algebraic groups (Memoirs of the American Mathematical Society, 80. American Mathematical Society, Providence, Rhode Island, 1980).Google Scholar