Equivariant Ulrich bundles on exceptional homogeneous varieties

Abstract

Abstract We prove that the only rational homogeneous varieties with Picard number 1 of the exceptional algebraic groups admitting irreducible equivariant Ulrich vector bundles are the Cayley plane E 6/P 1 and the E 7-adjoint variety E 7/P 1. From this result,we see that a general hyperplane section F 4/P 4 of the Cayley plane also has an equivariant but non-irreducible Ulrich bundle.