On domino insertion and Kazhdan--Lusztig cells in type Bn
Abstract
Based on empirical evidence obtained using the CHEVIE computer algebra system, we present a series of conjectures concerning the combinatorial description of the Kazhdan--Lusztig cells for type Bn with unequal parameters. These conjectures form a far-reaching extension of the results of Bonnaf\'e and Iancu obtained earlier in the so-called ``asymptotic case''. We give some partial results in support of our conjectures.
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