Homogeneous Ulrich bundles on isotropic flag varieties

In this paper, we consider the existence problem of Ulrich bundles on a rational homogeneous space $G\mathrm{/}P$ of type $B$, $C$ or $D$. We show that if the Picard number of $G\mathrm{/}P$ is greater than or equal to $2$, then there are no irreducible homogeneous Ulrich bundles on $G\mathrm{/}P$ with respect to the minimal ample class.