The Leading Coefficients for an Affine Weyl Group of Type
G
2
˜
: The Lowest Two-Sided Cell Case
This study focusses on the leading coefficients μ u , w of the Kazhdan–Lusztig polynomials P u , w for the lowest cell c 0 of an affine Weyl group of type G 2 ˜ and gives an estimation μ u , w ≤ 3 for u , w ∈ c 0 .