In the case where G is not compact , the representations have infinite dimension .
The notion of character is therefore more subtle to define since it is a Schwartz distribution ( represented by a locally integrable function ) , with singularities .
In the case where G is not compact , the representations have infinite dimension , and the notion of character is therefore more subtle to define since it is a Schwartz distribution ( represented by a locally integrable function ) , with singularities .