Non-trivial Kazhdan-Lusztig coefficients of affine Weyl groups

In this paper we show that the leading coefficients $mu(y,w)$ of some Kazhdan-Lusztig polynomials $P_{y,w}$ with $y,w$ in the affine Weyl group of type $widetilde{B_n}$ can be $n$; in the cases of types $widetilde{C_n}$ and $widetilde{D_n}$ they can be $n+1.$ Consequently, for the corresponding simply connected simple algebraic groups, the dimensions of the first extension groups between certain irreducible modules will go to infinity when $n$ increases.