Induction and Restriction of Kazhdan-Lusztig Cells

Barbasch and Vogan gave a beautiful rule for restricting and inducing Kazhdan-Lusztig representations of Weyl groups. In this paper we show that this rule implies and generalizes the Littlewood-Richardson rule for decomposing outer products of representations of the symmetric groups. A new recursive rule for computing characters of arbitrary Coxeter groups follows. Another application is a generalization of Garsia-Remmel's algorithm for decomposing certain tensor products of symmetric groups representations.