论文标题
扩展雪的算法用于有限的Weyl组计算
Extending Snow's algorithm for computations in the finite Weyl groups
论文作者
论文摘要
1990年，D.Snow提出了一种用于计算有限Weyl基团轨道的有效算法。 Snow的算法是为了计算Weyl组的重量，$ W $ - 器和元素的计算。提出了SNOW算法的扩展，该算法允许在同一运行时周期中找到一对相互反向元素以及计算$ W $ - 器的计算。这简化了Weyl组中共轭类别的计算。例如，给出了使用扩展雪的算法获得的Weyl Group $ W（D_4）$的元素的完整列表。 $ w（d_4）$的元素以两种方式指定：降低表达式和忠实表示的矩阵。我们将该小组的分区介绍为结合类，其元素指定为减少表达式。为$ W（D_4）$的共轭类别的代表提供了各种形式：使用Carter图，使用降低表达式并使用签名的周期类型。在附录中，我们提供了Python中该算法的实现。
In 1990, D.Snow proposed an effective algorithm for computing the orbits of finite Weyl groups. Snow's algorithm is designed for computation of weights, $W$-orbits and elements of the Weyl group. An extension of Snow's algorithm is proposed, which allows to find pairs of mutually inverse elements together with the calculation of $W$-orbits in the same runtime cycle. This simplifies the calculation of conjugacy classes in the Weyl group. As an example, the complete list of elements of the Weyl group $W(D_4)$ obtained using the extended Snow's algorithm is given. The elements of $W(D_4)$ are specified in two ways: as reduced expressions and as matrices of the faithful representation. We present a partition of this group into conjugacy classes with elements specified as reduced expressions. Various forms are given for representatives of the conjugacy classes of $W(D_4)$: using Carter diagrams, using reduced expressions and using signed cycle-types. In the appendix, we provide an implementation of the algorithm in Python.
