Lusztig's $a$-function for Coxeter groups with complete graphs
  We show that Lusztig's $a$-function of a Coxeter group is bounded if the Coxeter group has a complete graph (i.e. any two vertices are joined) and the cardinalities of finite parabolic subgroups of the Coxeter group have a common upper bound. 
Nanhua Xi
math.QA