# Quantization of Yang--Mills metrics on holomorphic vector bundles

## TL;DR

This paper explores the quantization of Hermitian metrics on holomorphic vector bundles over homogeneous Kähler manifolds, revealing strong stability properties of Yang--Mills metrics and their connections to operator theory.

## Contribution

It demonstrates that Yang--Mills metrics can be strongly quantized and introduces a new stability property for equivariant vector bundles surpassing Gieseker-stability.

## Key findings

- Yang--Mills metrics can be strongly quantized.
- Equivariant vector bundles exhibit a new stability property.
- Connections established between operator tuples and geometric vector bundles.

## Abstract

We investigate quantization properties of Hermitian metrics on holomorphic vector bundles over homogeneous compact K\"ahler manifolds. This allows us to study operators on Hilbert function spaces using vector bundles in a new way. We show that Yang--Mills metrics can be quantized in a strong sense and for equivariant vector bundles we deduce a strong stability property which supersedes Gieseker-stability. We obtain interesting examples of generalized notions of contractive, isometric, and subnormal operator tuples which have geometric interpretations related to holomorphic vector bundles over coadjoint orbits.