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Boundedness of Lusztig's $\boldsymbol{a}$-function for Coxeter groups of finite rank
We prove that there exists a bound $N'_L(W)$ for a positively weighted Coxeter group $(W, S, L)$ of finite rank. In particular, Lusztig's $\boldsymbol{a}$-function of $(W, S, L)$ is bounded.
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