Corollary 4

Let $\pi \in \widehat{G}$. The $\pi$-isotypical component of $\boldsymbol{\delta }_G$ (resp. the $\overline{\pi}$-isotypical component of $\boldsymbol{\gamma }_G$) is equal to $\boldsymbol{\varrho }_G(\pi )$.

The argument is similar to that of the preceding corollary, considering $\boldsymbol{\varrho }_G(\pi )$ as a subrepresentation of $\boldsymbol{\delta }_G$ (resp. of $\boldsymbol{\gamma }_G$).