  Kazhdan and Lusztig have shown that the partition of the symmetric group of
degree $n$ 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 for type $B_n$. We
also give an explicit description of the left cell representations and show
that they are irreducible and constructible.
