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This paper studies the Ulrich property of homogeneous vector bundles onrational homogenous varieties. We provide a criterion for an initializedirreducible homogeneous vector bundle on a rational homogeneous variety withany Picard number to be Ulrich with respect to any polarizations. Thiscriterion extends Fonarev's result, which applies to rational homogeneousvarieties with Picard number one. As an application, we show that rationalhomogeneous varieties with Picard number at least two of certain exceptionalalgebraic groups do not admit such homogeneous Ulrich bundles with respect tothe minimal ample class.

Homogeneous Ulrich bundles on homogenous varieties of certain exceptional types