Glider representations can be defined for a finite algebra filtration FKG determined by a chain of subgroups 1 ⊂ G₁ ⊂… ⊂ G_d = G. In this paper we develop the generalized character theory for such glider representations. We give the generalization of Artin’s theorem and define a generalized inproduct. For finite abelian groups G with chain 1 ⊂ G, we explicitly calculate the generalized character ring and compute its semisimple quotient. The papers ends with a discussion of the quaternion group as a first non-abelian example.

中文翻译：

---

组滑翔机表示的广义字符

滑翔机表示可以在有限的代数过滤来定义FKG确定由子组1⊂的链ģ ₁ ⊂...⊂ ģ _d = g ^。在本文中，我们为此类滑翔机表示开发了广义字符理论。我们对Artin定理进行了推广，并定义了广义乘积。对于有限阿贝尔群G ^与链1⊂ ģ，我们明确地计算广义字符环和计算其半单商数。论文最后以四元数组作为第一个非阿贝尔算例进行了讨论。