Frequent representations

Given a unitary representation $T$ of a finite group $G$ in $\mathbb C^n$, write $M$ for the variety of such representations which are unitary equivalent to $T$. The representation $T$ is said to be frequent if the dimension of the variety $M$ is maximal (among all representations of $G$ in the same complex space). We prove that the irreducible representations are distributed, in the frequent representation (of large dimension), asymptotically in the same way as in the fundamental representation in the space of functions on $G$: the frequencies of the irreducible components are proportional to their dimensions.