On Kazhdan-Lusztig cells in type $B$.
Journal of Algebraic Combinatorics, Tome 31 (2010) no. 1, pp. 53-82.

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Summary: We prove that, for any choice of parameters, the Kazhdan-Lusztig cells of a Weyl group of type $B$ are unions of combinatorial cells (defined using the domino insertion algorithm).
Keywords: keywords Weyl group, type B, Kazhdan-Lusztig theory, unequal parameters, cells
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     author = {Bonnaf\'e, C\'edric},
     title = {On {Kazhdan-Lusztig} cells in type $B$.},
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Bonnafé, Cédric. On Kazhdan-Lusztig cells in type $B$.. Journal of Algebraic Combinatorics, Tome 31 (2010) no. 1, pp. 53-82. http://geodesic.mathdoc.fr/item/JAC_2010__31_1_a5/