Equivariant Ulrich bundles on exceptional homogeneous varieties

Abstract

© 2021 Walter de Gruyter GmbH, Berlin/Boston 2021.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 E6/P1 and the E7-adjoint variety E7/P1. From this result,we see that a general hyperplane section F4/P4 of the Cayley plane also has an equivariant but non-irreducible Ulrich bundle.