Algorithmic aspects of semistability of quiver representations
<|reference_start|>Algorithmic aspects of semistability of quiver representations: We study the semistability of quiver representations from an algorithmic perspective. We present efficient algorithms for several fundamental computational problems on the semistability of quiver representations: deciding semistability and $\sigma$-semistability, finding maximizers of King's criterion, and finding the Harder-Narasimhan filtration. We also investigate a class of polyhedral cones defined by the linear system in King's criterion, which we call King cones. We demonstrate that the King cones for rank-one representations can be encoded by submodular flow polytopes, allowing us to decide the $\sigma$-semistability of rank-one representations in strongly polynomial time. Our argument employs submodularity in quiver representations, which may be of independent interest.<|reference_end|>
@article{iwamasa2024algorithmic,
    title={Algorithmic aspects of semistability of quiver representations},
    author={Yuni Iwamasa and Taihei Oki and Tasuku Soma},
    journal={arXiv preprint arXiv:2407.06493},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.06493},
    primaryClass={math.OC cs.DM cs.DS math.CO math.RT}
}