%0 Journal Article
%T <sub>C</sub><sup style="margin-left:-9px;">~</sup><sub>3</sub>型仿射Weyl群中的Φ值<br>The Value of Φ in the Affine Weyl Group of Type <sub>C</sub><sup style="margin-left:-9px;">~</sup><sub>3</sub>
%A 王雨露
%A 王利萍
%A 何厚智
%J Pure Mathematics
%P 3475-3480
%@ 2160-7605
%D 2023
%I Hans Publishing
%R 10.12677/PM.2023.1312361
%X 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<sub>C</sub><sup>~</sup><sub>3</sub>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。<br />
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 <sub>C</sub><sup>~</sup><sub>3</sub>. These results lay the foundation for further calculating certain Kazhdan-Lusztig coefficients of the group.
%K 仿射Weyl群，半线性方程组，Φ值<br>Affine Weyl Group
%K Semi-Linear Equation System
%K The Value of Φ
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=77893