PreprintCC BY 4.0arXiv
Harder-Narasimhan Filtrations of Hyperquiver Representations
Abstract
Hyperquiver representations are generalisations of quiver representations. They are directed hypergraphs with vector spaces assigned to vertices, and for every directed hyperedge, an assignment of a linear map from the tensor product of the source vector spaces to the tensor product of the target vector spaces. We study the moduli of hyperquiver representations, where we use affine GIT to describe the (in)stability of such objects under the action of a product of general linear groups. Our main result introduces the Harder-Narasimhan filtration of a hyperquiver representation. We also derive a formula for the weights of this unique filtration, which specialise to the Harder-Narasimhan slopes of a quiver representation.
Related
- Surjectivity of real-linear Cauchy--Riemann operators: from the minimal Harder--Narasimhan slope to automatic transversality
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BibTeX
@misc{muller2026hardernarasimhan,
title = {{Harder-Narasimhan Filtrations of Hyperquiver Representations}},
author = {Tommi Muller},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28028},
eprint = {2610.28028},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28028},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Harder-Narasimhan Filtrations of Hyperquiver Representations
AU - Tommi Muller
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28028
UR - https://arxiv.org/abs/2610.28028
AB - Hyperquiver representations are generalisations of quiver representations. They are directed hypergraphs with vector spaces assigned to vertices, and for every directed hyperedge, an assignment of a linear map from the tensor product of the source vector spaces to the tensor product of the target vector spaces. We study the moduli of hyperquiver representations, where we use affine GIT to describe the (in)stability of such objects under the action of a product of general linear groups. Our main result introduces the Harder-Narasimhan filtration of a hyperquiver representation. We also derive a formula for the weights of this unique filtration, which specialise to the Harder-Narasimhan slopes of a quiver representation.
ER -