Homogeneous Ulrich bundles on Flag manifolds
L. Costa, R.M. Mir\'o-Roig

TL;DR
This paper investigates the existence and classification of irreducible homogeneous Ulrich bundles on various flag manifolds, providing explicit counts and non-existence results for specific cases.
Contribution
It classifies irreducible homogeneous Ulrich bundles on certain flag manifolds and establishes counts and non-existence results, proposing a conjecture for general cases.
Findings
All irreducible homogeneous Ulrich bundles on $f(0,n-1,n)$ are classified, with exactly $2^{n-1}$ such bundles.
Identifies specific flag manifolds supporting irreducible homogeneous Ulrich bundles, such as $f(0,n-2,n)$ and $f(1,n-1,n)$.
Proves the non-existence of such bundles on $f(0,1,n)$.
Abstract
Let be a -vector space of dimension . In this paper, we focus our attention into the existence of irreducible homogeneous Ulrich bundles on flag manifolds which parameterizes all chains of linear subspaces of dimension , respectively. We determine all irreducible homogeneous Ulrich bundles on and we prove that there are exactly . Similarly, we prove that and are also the support of irreducible homogeneous Ulrich bundles. On the other hand, we prove that do not support any irreducible homogeneous Ulrich bundle. We end posing a conjecture concerning the existence of irreducible homogeneous Ulrich bundles on in terms of and .
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Geometry and complex manifolds
