Left cells in type 𝐵_{𝑛} with unequal parameters

Abstract

Kazhdan and Lusztig have shown that the partition of the symmetric group S n {\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 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 B_n . We provide an explicit description of the left cell representations and show that they are irreducible and constructible.