  We investigate many-body effects on a mixture of interacting bosons and
fermions loaded in an optical lattice using a generalized dynamical mean field
theory combined with the numerical renormalization group. We show that strong
correlation effects emerge in the presence of bosonic superfluidity, leading to
a renormalized peak structure near the Fermi level in the density of states for
fermions. Remarkably, this kind of strong renormalization appears not only in
the metallic phase but also in the insulating phases of fermions such as in the
empty/filled band limit. A systematic analysis of the relation between the
quasiparticle weight and the strength of superfluidity reveals that the
renormalization effect is indeed caused by the boson degrees of freedom. It is
found that such renormalization is also relevant to a supersolid phase
consisting of a density wave ordering of fermions accompanied by bosonic
superfluidity. This sheds light on the origin of the peak structure in the
supersolid phase.
