  The underscreened Kondo lattice consisting of a single twofold degenerate
conduction band and a CEF split 4f-electron quasi-quartet has non-conventional
quasiparticle dispersions obtained from the constrained mean-field theory. An
additional genuinely heavy band is found in the main hybridization band gap of
the upper and lower hybridzed bands whose heavy effective mass is controlled by
the CEF splitting. Its presence should profoundly influence the dynamical
optical and magnetic response functions. In the former, the onset of the
optical conductivity is not the main hybridisation energy but the much lower
Kondo energy scale which appears in the direct transitions to the additional
heavy band. The dynamical magnetic response is also strongly modified by the
in-gap heavy band which can lead to unconventional resonant excitations that
may be interpreted as coherent CEF-Kondo lattice magnetic exciton bands. Their
instability at low temperature signifies the onset of induced excitonic
magnetism in the underscreened Kondo lattice.
