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Cells for two Coxeter groups. (English) Zbl 0608.20037

The decompositions of the affine Weyl group \(W(\tilde C_ 3)\) into left cells and into two-sided cells [cf. D. Kazhdan and G. Lusztig, Invent. Math. 53, 165-184 (1979; Zbl 0499.20035)] are given, and it is shown that the hyperbolic rank 3 Coxeter group W(M), where \(M=(m_{ij})_{1\leq i,j\leq 3}\) is the Coxeter matrix determined by \(m_{12}=m_{13}=3\) and \(m_{23}=4\), has infinitely many left cells.
Reviewer: A.M.Cohen

MSC:

20H15 Other geometric groups, including crystallographic groups
20G05 Representation theory for linear algebraic groups

Citations:

Zbl 0499.20035
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References:

[1] Bourbaki N., Groupes et Algebres de Lie (1968) · Zbl 0186.33001
[2] DOI: 10.1007/BF01390031 · Zbl 0499.20035 · doi:10.1007/BF01390031
[3] Lusztig G., Cells in Affine Weyl Groups · Zbl 0569.20032
[4] Lusztig G., Trans. Amer. Math. Soc 277 pp 623– (1983)
[5] DOI: 10.1007/BF01418931 · Zbl 0244.17005 · doi:10.1007/BF01418931
[6] Shi J.Y., Ph.D. Thesis (1984)
[7] Spaltenstein N., Lect. Notes in Math 946 (1982)
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