Higher discriminants of vector bundles and Schur functors

Abstract

We prove some closed formulas for the logarithmic Chern character of a locally free sheaf. The argument used is representation-theoretic and we connect these formulas with the actions of some Casimir elements of ${\mathfrak{sl}}_r$. As an application, we give a recipe to construct slope polystable modular bundles on hyper-Kähler manifolds from old ones.

22 pages. Comments are very welcome!