= Evaluation adjunction for unnormalized induction
{title2=$\operatorname{Hom}_G(W,\operatorname{Ind}_B^G\xi)\cong\operatorname{Hom}_B(W,\xi)$}
Evaluation of an intertwiner at the identity gives a $B$-equivariant functional. Conversely a functional $\ell$ gives $A(v)(g)=\ell(\pi(g)v)$, which has the required covariance and is fixed on the right by any <compact-open subgroup> fixing $v$. These inverse constructions prove the displayed adjunction. If $\xi$ is trivial on the unipotent radical, it is equivalent to a character-valued functional on the <Jacquet module>.
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