Résumé
To each finite Coxeter system (W,S) and to each weight function L, Lusztig
has defined the notions of constructible characters and of Lusztig families of
W, using the so-called J-induction. Whenever L is constant, and using a general
argument, Lusztig has shown that all Lusztig family contains a unique character
with minimal b-invariant, and that every constructible character contains an
irreducible constituent with minimal b-invariant. We show in this paper that
this can be generalized to the case where L is not constant: our proof is by a
case-by-case analysis.