  We study the principal parts bundles $P^k (L)$ of the degree $d$ line bundle
$L$ on the $n$ dimensional projective space as homogeneous bundles and we
describe their associated quiver representations. We use this approach to show
that if $n$ is greater or equal that 2, and $0\leq d<k$, then there exists an
invariant splitting $P^k(L)=Q\oplus (S^dV\otimes \OO_{\PP^n})$ with $Q$ a
stable homogeneous vector bundle. The splitting properties of such bundles were
previously known only for n=1 or $k\leq d$ or $d<0$. Moreover we show that for
any $d$ and any $h<k$ the canonical map from $P^k(L)$ to $P^h(L)$ always
induces a linear map on the spaces of global sections which has maximal rank.
