  This work re-examines the issue of spin-$1$ particles in a
($2+1$)-dimensional Duffin-Kemmer-Petiau oscillator (DKPO) in the presence of
an external magnetic field. By following the appropriate procedure for the
spin-$1$ sector of the Duffin-Kemmer-Petiau (DKP) theory, the previously used
$6\times 6$ representation in the literature is shown to be reducible to a
$3\times 3$ irreducible representation. This approach enabled us to find new
aspects of the results recently disseminated in various studies, as well as
other considerations overlooked and requiring revision. Finally, we present
some applications of two-dimensional DKP theory in condensed matter systems,
particularly in Lieb lattices.
