Homogeneous Ulrich bundles on Flag manifolds

الأصل · EN

Let V be a K-vector space of dimension n+1. In this paper, we focus our attention into the existence of irreducible homogeneous Ulrich bundles on flag manifolds (p, q,n) which parameterizes all chains of linear subspaces Lₚ ⊂ Lq ⊂ (V) of dimension p< q, respectively. We determine all irreducible homogeneous Ulrich bundles on (0,n-1,n) and we prove that there are exactly 2ⁿ⁻¹. Similarly, we prove that (0,n-2,n) and (1,n-1,n) are also the support of irreducible homogeneous Ulrich bundles. On the other hand, we prove that (0,1,n) do not support any irreducible homogeneous Ulrich bundle. We end posing a conjecture concerning the existence of irreducible homogeneous Ulrich bundles on (p,q,n) in terms of p and q.