■型仿射Weyl群中aλ,λ′的计算

Calculations of aλ,λ′ in the Affine Weyl Group of Type ■

为了研究仿射Weyl群W-图的非局部有限性,Lusztig引入了与Kazhdan-Lusztig(以下简称“K-L”)多项式的首项系数μ(y,w)相关的一些半线性方程,这些半线性方程对于求解仿射Weyl群的首项系数起着重要作用.通过分析A3型仿射Weyl群的相关结构,主要计算了半线性方程中的aλ,λ′,这些结果在求解其所对应的K-L多项式的首项系数中起着决定性的作用.

In order to study the nonlocal finiteness of W-graphs in affine Weyl groups,Lusztig introduced some semi-linear equations related to the leading coefficientsμ(y,w)of the Kazhdan-Lusztig(abbreviated as“K-L”)polynomials.These semi-linear equations play an important role in solving the leading coefficients of affine Weyl groups.By analyzing the related structures of the affine Weyl group of type A3,the aλ,λ′in semi-linear equations is mainly calculated,which plays a decisive role in solving the leading coefficients of the corresponding K-L polynomials.