Finite Dimensional Group Representations

Algebraic relations among matrices, if any, are encapsulated in their characteristic polynomial. How to decipher this information thus becomes an appealing question. A good place to start an investigation is where the matrices generate a group. Although the exact form of characteristic polynomial varies with respect to the change of generating sets, some of its properties are closely linked with the inherent algebraic structure of the group. This chapter recalls the pioneer work of Dedekind and Frobenius and examines the issue for abelian or Coxeter groups.