Principal parts bundles on projective spaces and quiver representations

We study the principal parts bundles PkOℙn(d) as homogeneous bundles and we describe their associated quiver representations. With this technique we show that if n ≥ 2 and 0 ≤ d < k then there exists an invariant decomposition PkOℙn(d) = Qk,d ⊕ (SdV ⊗ Oℙn) with Qk,d a stable homogeneous vector bundle. The decomposition properties of such bundles were previously known only for n = 1 or k ≤ d or d < 0. Moreover we show that the Taylor truncation maps H0PkOℙn(d)→H0PhOℙn(d), defined for any h ≤ k and any d, have maximal rank.