The structure of the space of affine Kaehler curvature tensors as a complex module

TL;DR

This paper decomposes the space of affine Kaehler curvature tensors into irreducible modules using complex representation theory, building on previous results by Matzeu and Nikcevic.

Contribution

It provides a new decomposition of affine Kaehler curvature tensors as a complex module, advancing understanding of their algebraic structure.

Findings

Decomposition of the tensor space into irreducible modules

Extension of previous results to the complex setting

Enhanced understanding of affine Kaehler geometry

Abstract

We use results of Matzeu and Nikcevic to decompose the space of affine Kaehler curvature tensors as a direct sum of irreducible modules in the complex setting