Abstract
We develop a general theory of quiver representations $\mathcal{F}$ which is motivated by investigating group representations in different characteristics simultaneously. A feature of $\mathcal{F}$ is to assign to each vertex $a$ of the quiver a finite set $\mathcal{F}_{a}$. This result provides a uniform explanation of many objects in group character theory. Furthermore, we give a characterization of when the prime graph $\Gamma(G)$ of a finite group $G$ is disconnected by using group characters. And then, this result on $\Gamma(G)$ can be rephrased in terms of certain quiver representations.
Citation
Nobuo IIYORI. Masato SAWABE. "Quiver Representations, Group Characters, and Prime Graphs of Finite Groups." Tokyo J. Math. 42 (2) 497 - 523, December 2019. https://doi.org/10.3836/tjm/1502179297