Left cells in type 𝐵_{𝑛} with unequal parameters

Bonnafé, Cédric; Iancu, Lacrimioara

doi:10.1090/S1088-4165-03-00188-2

Left cells in type $B_n$ with unequal parameters
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by Cédric Bonnafé and Lacrimioara Iancu

Represent. Theory 7 (2003), 587-609

DOI: https://doi.org/10.1090/S1088-4165-03-00188-2

Published electronically: November 19, 2003

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Abstract:

Kazhdan and Lusztig have shown that the partition of the symmetric group ${\mathfrak {S}}_n$ into left cells is given by the Robinson–Schensted correspondence. The aim of this paper is to provide a similar description of the left cells in type $B_n$ for a special class of choices of unequal parameters. This is based on a generalization of the Robinson–Schensted correspondence in type $B_n$. We provide an explicit description of the left cell representations and show that they are irreducible and constructible.

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