In this talk I will discuss some topics arising from dealing with representations of finite groups in characteristic 0, in particular over the rational field or algebraic number fields.
The main theme is the decomposition of representations into their irreducible constituents. Powerful computational methods for this task are available over finite fields (the MeatAxe), but they do not carry over easily due to the infiniteness of the rational field. However, in many cases surprisingly simple methods turn out to be surprisingly efficient.
On the other hand, it is easy to find examples where basically everything fails. These give rise to some interesting open questions.
