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On domino insertion and Kazhdan--Lusztig cells in type $B_n$

Cédric Bonnafé·Meinolf Geck·Lacrimioara Iancu·Thomas Lam
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Abstract

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

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Cédric Bonnafé, Meinolf Geck, Lacrimioara Iancu, Thomas Lam. 2007-03-19. On domino insertion and Kazhdan--Lusztig cells in type $B_n$. https://arxiv.org/abs/math/0609279

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