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

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

2006-09-11

arxiv.org/abs/math/0609279v2

Mathematics

Representation Theory

22 pages; minor corrections

Scientific paper

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 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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