Bédard, Robert Cells for two Coxeter groups. (English) Zbl 0608.20037 Commun. Algebra 14, 1253-1286 (1986). 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 Cited in 3 ReviewsCited in 24 Documents MSC: 20H15 Other geometric groups, including crystallographic groups 20G05 Representation theory for linear algebraic groups Keywords:decompositions; affine Weyl group; left cells; hyperbolic rank 3 Coxeter group Citations:Zbl 0499.20035 PDFBibTeX XMLCite \textit{R. Bédard}, Commun. Algebra 14, 1253--1286 (1986; Zbl 0608.20037) Full Text: DOI 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) 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.