This work demonstrates that tensor products of polystable quiver bundles are polystable, suggesting deeper links to quiver representations and varieties.
In this work, we introduce a notion of tensor product of (twisted) quiver representations with relations in the category of OX-modules. As a first application of our notion, we see that tensor products of polystable quiver bundles are polystable and later we use this to both deduce a quiver version of the Segre embedding and to identify distinguished closed subschemes of GL(n,C)-character varieties of free abelian groups.
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Juan Sebastian Numpaque-Roa (2025) studied this question.
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