摘要
Kazhdan-Lusztig多项式的首项系数在表示理论与李理论中有着非常重要的地位。 Lusztig在研究W -图的非局部有限性时引入的半线性方程组是计算Kazhdan-Lusztig多项式首项系数的重要方法。 本文给出了一个计算任意型的仿射Weyl群中Φ值的程序设计思路,并给出了一个利用Matlab程序计算A~44型仿射Weyl群中所有Φ值的例子,输出结果表明,A~44型仿射Weyl群只有291个非零且各不相同的Φ值。
The leading coefficients of Kazhdan-Lusztig polynomials are of great importance in representation theory and Lie theory. The system of semi-linear equations introducedby Lusztig in his study of nonlocal finiteness of W-graphs is an important method forcomputing the leading coefficients of Kazhdan-Lusztig polynomials. In this paper, wegive a design idea of a program to compute the Φ values in an affine Weyl group ofarbitrary type, and give an example of computing all the Φ values in an affine Weylgroup of type A~44 using a Matlab program. The output shows that the affine Weylgroup of type A~44 has only 291 non-zero and distinct Φ values.
出处
《理论数学》
2024年第7期94-102,共9页
Pure Mathematics
