Matlab程序在计算仿射Weyl群Φ值中的应用
Application of Matlab to Calculate ΦValues of Affine Weyl Groups
DOI: 10.12677/PM.2024.147276, PDF, 下载: 1  浏览: 5  科研立项经费支持
作者: 何厚智, 王利萍, 王雨露：北京建筑大学理学院，北京
关键词: 仿射Weyl群；首项系数；Φ值；Matlab；Affine Weyl Groups； Leading Coefficient； Φ Value； Matlab
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。
Abstract: The leading coefficients of Kazhdan-Lusztig polynomials are of great importance in representation theory and Lie theory. The system of semi-linear equations introduced by Lusztig in his study of nonlocal finiteness of W-graphs is an important method for computing the leading coefficients of Kazhdan-Lusztig polynomials. In this paper, we give a design idea of a program to compute the Φ values in an affine Weyl group of arbitrary type, and give an example of computing all the Φ values in an affine Weyl group of type A~44 using a Matlab program. The output shows that the affine Weyl group of type A~44 has only 291 non-zero and distinct Φ values.
文章引用：何厚智, 王利萍, 王雨露. Matlab程序在计算仿射Weyl群Φ值中的应用[J]. 理论数学, 2024, 14(7): 94-102. https://doi.org/10.12677/PM.2024.147276

参考文献

[1] Kazhdan, D. and Lusztig, G. (1980) Schubert Varieties and Poincare Duality. In: Osserman, R. and Weinstein, A., Eds., Geometry of the Laplace Operator, AMS, 185-203.
https://doi.org/10.1090/pspum/036/573434
[2] Lusztig G. (1985) Cells in Affine Weyl Groups. Algebraic Groups and Related Topics, 6, 255- 287.
https://doi.org/10.2969/aspm/00610255
[3] Lusztig, G. (1996) Nonlocal Finiteness of a W-Graph. Representation Theory of the American Mathematical Society, 1, 25-30.
https://doi.org/10.1090/s1088-4165-97-00003-4
[4] 王利萍. A~2型和B~2型仿射Weyl 群的Kazhdan-Lusztig多项式的首项系数[D]: [博士学位论文]. 北京: 中国科学院研究生院(数学与系统科学研究院), 2008.
[5] 郭鹏飞. G~2型仿射Weyl 群的Kazhdan-Lusztig多项式的首次系数[D]: [博士学位论文]. 广州: 华南理工大学, 2015.
[6] 代佳华, 王利萍, 魏玉丽. G~3型仿射Weyl群最低双边胞腔上的Kazhdan-Lusztig系数[J]. 数学的实践与认识, 2021, 51(19): 264-271.
[7] 魏玉丽, 王利萍, 罗新, 等. A～3型仿射Weyl 群最低双边胞腔上的Kazhdan-Lusztig系数[J]. 数学 的实践与认识, 2021, 51(3): 290-301.
[8] Kazhdan, D. and Lusztig, G. (1979) Representations of Coxeter Groups and Hecke Algebras. Inventiones Mathematicae, 53, 165-184.
https://doi.org/10.1007/BF01390031

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