数学史的研究以往多集中在对历史事件的描述，但为重大数学事件寻找历史根源亦是数学史研究的任务，有限群表示论的创立就深刻影响了20世纪数学的发展面貌。一门新学科的建立需要有新问题的产生、新思想的出现以及新工具的应用，研究一门新学科的创立过程就需要通过对这三个方面的研究来解释新学科创立的内在动因。对有限群表示理论创立过程的研究包括前史部分和创立过程两部分。前史部分包括群行列式的产生背景、“表示”思想的来源以及19世纪的矩阵理论；在创立过程主要研究Dedekind和Frobenius的群行列式工作以及由此产生的群表示理论。通过这两部分的结合，分析群表示论创立的内部原因，回答为什么有限群表示论会于19世纪末诞生的问题。

In the past, the study of the history of mathematics often focus on the description of the historical events, but to find reasons for a major mathematical event is also the task of the research. The establishment of the representation theory of finite group has deeply influenced on the development of the mathematics of twentieth century. The establishment of a new subject needs to have new problems, new ideas and new tools to applicated. To study the establishment process has to be used to explain the internal motivation of the new subject in the three aspects. The study of the process for representation theory of finite group founded includes former history part and early process part. Former history part includes the group determinant, the idea of “represent” and the matrix theory of 19th century; early process part focus in Dedekind and Frobenius’s work on group determinant and with which produced representation theory of group. Through the combination of the two parts, this paper analyzes the reason of the emergence of the representation theory, and then try to answer the question: why the representation theory of finite group had born in the end of the 19th century?