I am new to character theory and I have the following question.
In the dual group of a groupe $G$ we can define an inner product. This inner product is equal to :
$$\dim Hom_G(a,b) $$
The problem is that I don’t understand what it means. I know that the dimension of a representation $p : G \to GL(V)$ is equal to $\dim(V)$. So here in the dual group very element has dimension $1$ (since $V = \mathbb{C}^*$).
Yet, here what does it mean to take the dimension of a morphisme between two representations ?
Thanks you !