_C~₃型仿射Weyl群中的Φ值  

The Value of Φ in the Affine Weyl Group of Type C~3

作　　者：王雨露 王利萍 何厚智 

机构地区：[1]北京建筑大学理学院,北京

出　　处：《理论数学》2023年第12期3475-3480,共6页Pure Mathematics

摘　　要：半线性方程组是计算仿射Weyl群Kazhdan-Lusztig系数的重要工具,而Φ值是求解半线性方程组的一个重要变量。对于Φ值的计算,成为研究Kazhdan-Lusztig系数的关键环节。本文综合利用李代数表示理论中的权格、根格,及计算机编程,对于C~3型仿射Weyl群,计算得出了全部的Φ值。这些结果对于进一步计算该群的某些Kazhdan-Lusztig系数奠定了基础。A system of semi-linear equations is an important tool for calculating the Kazhdan-Lusztig coeffi-cients of affine Weyl groups, and the value of Φ is an important variable in solving the system of semi-linear equations. The calculation of values of Φ has become a key link in studying the Kazhdan-Lusztig coefficients. In this article, by comprehensively using the weight lattice, root lattice in the representation theory of Lie algebras, and computer programming, we get all values of Φ for affine Weyl group of type C~3. These results lay the foundation for further calculating certain Kazhdan-Lusztig coefficients of the group.

关 键 词：仿射WEYL群 半线性方程组 Φ值 

分 类 号：O15[理学—数学]