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PreprintarXiv licencearXiv

Invariant Jacobian and the Center of a Homogeneous Form

  • Yue Hu
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Abstract

We study homogeneous forms with invariant Jacobian under group actions. For finite-dimensional irreducible complex representations, we show that the canonical decomposition defined by the center of the form is either trivial or gives a system of imprimitivity, which determines the module structure of Jacobian J(f). We apply the theory to symmetric groups and classify homogeneous forms with invariant Jacobian on the natural permutation module.

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Cite

BibTeXRIS
BibTeX
@misc{hu2026invariant,
  title = {{Invariant Jacobian and the Center of a Homogeneous Form}},
  author = {Yue Hu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.06719},
  eprint = {2609.06719},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.06719},
}
RIS
TY  - UNPB
TI  - Invariant Jacobian and the Center of a Homogeneous Form
AU  - Yue Hu
PY  - 2026
DA  - 2026/09/06
PB  - arXiv
DO  - 10.48550/arxiv.2609.06719
UR  - https://arxiv.org/abs/2609.06719
AB  - We study homogeneous forms with invariant Jacobian under group actions. For finite-dimensional irreducible complex representations, we show that the canonical decomposition defined by the center of the form is either trivial or gives a system of imprimitivity, which determines the module structure of Jacobian J(f). We apply the theory to symmetric groups and classify homogeneous forms with invariant Jacobian on the natural permutation module.
ER  -