On Negative Orbits of Finite Coxeter Groups
Sarah B. Perkins
and Peter J. Rowley
DOI: 10.1023/B:JACO.0000047290.27248.c8
Abstract
For a Coxeter group W, X a subset of W and 
a positive root, we define the negative orbit of under X to be { w ; | w 
X} 
-, where - is the set of negative roots. Here we investigate the sizes of such sets as varies in the case when W is a finite Coxeter group and X is a conjugacy class of W.
a positive root, we define the negative orbit of under X to be { w ; | w X} -, where - is the set of negative roots. Here we investigate the sizes of such sets as varies in the case when W is a finite Coxeter group and X is a conjugacy class of W.Pages: 17–31
Keywords: Coxeter group; root system
Full Text: PDF
References
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2. J.J. Cannon and C. Playoust, An Introduction to Algebraic Programming with MAGMA [draft], Springer-Verlag, 1997.
3. R.W. Carter, “Conjugacy classes in the Weyl group,” Compositio. Math. 25 (1972), 1-59.
4. J.E. Humphreys, “Reflection groups and coxeter groups,” Cambridge Studies in Advanced Mathematics 29 (1990).
5. S.B. Perkins and P.J. Rowley, Coxeter Length, J. Algebra 273(1) (2004), 344-358.
2. J.J. Cannon and C. Playoust, An Introduction to Algebraic Programming with MAGMA [draft], Springer-Verlag, 1997.
3. R.W. Carter, “Conjugacy classes in the Weyl group,” Compositio. Math. 25 (1972), 1-59.
4. J.E. Humphreys, “Reflection groups and coxeter groups,” Cambridge Studies in Advanced Mathematics 29 (1990).
5. S.B. Perkins and P.J. Rowley, Coxeter Length, J. Algebra 273(1) (2004), 344-358.