  We systematically consider the AdS/CFT correspondence for a simplest
mixed-symmetry massless gauge field described by hook Young diagram. We
introduce the radial gauge fixing and explicitly solve the Dirichlet problem
for the hook field equations. Solution finding conveniently splits in two
steps. We first define an incomplete solution characterized by a functional
freedom and then impose the boundary conditions. The resulting complete
solution is fixed unambiguously up to boundary values. Two-point correlation
function of hook primary operators is found via the corresponding boundary
effective action computed separately in even and odd boundary dimensions. In
particular, the higher-derivative action for boundary conformal hook fields is
identified with a singular part of the effective action in even dimensions. The
bulk/boundary symmetry transmutation within the Dirichlet boundary problem is
explicitly studied. It is shown that traces of boundary fields are
Stueckelberg-like modes that can be algebraically gauged away so that boundary
fields are traceless.
