Left translation of a group function
= Left translation of a group function
{title2=$(L_af)(x)=f(a^{-1}x)$}
For a scalar function on a <group>, left translation by $a$ is $(L_af)(x)=f(a^{-1}x)$. With the positive-representation convention for <Fourier analysis on a finite group>, $\widehat{L_af}(\rho)=\rho(a)\widehat f(\rho)$.