Quandles with orbit series conditions

幂零轨道列

Series of nilpotent orbits

利用triality模型将特殊复李代数中的幂零轨道组织成级数，并证明了在每个级数中，对于f_4，e_6，e_7，e_8，轨道的维数分别是自然参数a= 1，2，4，8的线性函数.我们还以统一的方式获得明确的代表。我们观察到类似的中心化子的幂零元元在一个系列和分次组件在相关的分次的环境李代数。更引人注目的是，对于一个大于1，相应的Chevalley群的幂幺特征的次数，通过施普林格对应关系与这些级数相关联，由多项式给出，这些多项式具有关于a的统一表达式。

Coxeter group actions and limits of hypergeometric series

In this paper, we use combinatorial group theory and a limiting process to connect various types of hypergeometric series, and of relations among such series. We begin with a set $S$ of 56 distinct translates of a certain function $M$, which takes the form of a Barnes integral, and is expressible as a sum of two very-well-poised $_9F_8$ hypergeometric series of unit argument. We consider a known, transitive action of the Coxeter group $W(E_7)$ on this set. We show that, by removing from $W(E_7)$ a particular generator, we obtain a subgroup that is isomorphic to $W(D_6)$, and that acts intransi…

从一个映射和轨道等价中得到的群

A group from a map and orbit equivalence

本文研究逆向问题，探讨 $S^1$ 上扩张分段同胚成为某群“Bowen-Series型”映射的动力学条件及可能出现的群，并给出部分解答。

Relations among complementary and supplementary pairings of Saalschutzian 4F3(1) series

We investigate sums $K(\vec{x})$ and $L(\vec{x})$ of pairs of (suitably normalized) Saalschützian ${}_4F_3(1)$ hypergeometric series, and develop a theory of relations among these $K$ and $L$ functions. The function $L(\vec{x})$ has been studied extensively in the literature, and has been shown to satisfy a number of two-term and three-term relations with respect to the variable $\vec{x}$. More recent works have framed these relations in terms of Coxeter group actions on $\vec{x}$, and have developed a similar theory of two-term and three-term relations for $K(\vec{x})$. In this article, we de…