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This paper studies the Kazhdan-Lusztig coefficients $\mu(u,w)$ of theKazhdan-Lusztig polynomials $P_{u,w}$ for the lowest cell ${c_{0}}$ of anaffine Weyl group of type $\widetilde{G_{2}}$ and gives an estimation$\mu(u,w)\leqslant 3$ for $u,w\in c_{0}$.

Kazhdan-Lusztig coefficients for the lowest two-sided cell of type $\tilde{G_{2}}$