Induction and restriction of Kazhdan-Lusztig cells (Q1265473)

\textit{D. Barbasch} and \textit{D. Vogan} introduced a rule for restriction and induction of Kazhdan-Lusztig representations of Weyl groups [J. Algebra 80, 350-382 (1983; Zbl 0513.22009)]. In the paper under review, the author uses this rule to imply the Littlewood-Richardson rule for decomposing outer products of representations of the symmetric groups. Furthermore, he generalizes the latter to arbitrary Coxeter groups. Regarding the Murnaghan-Nakayama rule for characters of the symmetric groups as a result of the Littlewood-Richardson rule, the author uses a generalized Littlewood-Richardson rule to get a recursion theorem for the Kazhdan-Lusztig characters of arbitrary Coxeter groups. \textit{M.-P. Schützenberger} suggested a new version to the Littlewood-Richardson rule in terms of Knuth equivalence classes [Lect. Notes Math. 579, 59-113 (1977; Zbl 0398.05011)]. Then \textit{A. M. Garsia} and \textit{J. Remmel} applied Schützenberger's version to obtain a combinatorial procedure for decomposing tensor products of representations of symmetric groups [Graphs Comb. 1, 217-263 (1985; Zbl 0588.05005)]. In this paper, by applying the Barbasch-Vogan rule, the author generalizes Garsia-Remmel's result to other Weyl groups.