On Kazhdan-Lusztig cells in type B
C\'edric Bonnaf\'e (LM-Besan\c{c}on)
TL;DR
This paper proves that Kazhdan-Lusztig cells in type B Weyl groups are unions of combinatorial cells defined via domino insertion, confirming a conjecture across all parameters.
Contribution
It establishes that Kazhdan-Lusztig cells in type B are unions of combinatorial cells for any parameters, linking algebraic and combinatorial structures.
Findings
Kazhdan-Lusztig cells in type B are unions of combinatorial cells
The result holds for all parameter choices
Confirms a conjecture relating algebraic and combinatorial cells
Abstract
We prove that, for any choice of parameters, the Kazhdan-Lusztig cells of a Weyl group of type are unions of combinatorial cells (defined using the domino insertion algorithm).
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