Deformed Hermitian-Yang-Mills equation on the manifold of full flags

Abstract

We construct the first example of a higher rank, irreducible deformed Hermitian-Yang-Mills (dHYM) connection in the small radius regime. We also construct these in the large radius regime on infinitely many different bundles and make some contributions to the rank one equation as well. In particular, we investigate solutions away from the supercritical regime, showing the existence of solutions with any possible angle, and rule out some possible stability conditions.