Lusztig's $a$ -function for Coxeter groups with complete graphs

preprint2011arXivOpen access

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.

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Lusztig's $a$ -function for Coxeter groups with complete graphs

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Lusztig's aaa-function for Coxeter groups with complete graphs

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Lusztig's $a$ -function for Coxeter groups with complete graphs