character কী?

The character of $(V, \rho)$ is $\chi_\rho(g) = \operatorname{tr}\rho(g)$. It satisfies $\chi_\rho(e) = \dim V$, $\chi_\rho(hgh^{-1}) = \chi_\rho(g)$ (traces are conjugation-invariant): characters are class functions — elements of the space $\mathcal{CF}(G)$ of functions constant on conjugacy classes, equipped with the Hermitian inner product