Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Hu, Yue
Institution: Beijing University of Posts and Telecommunications
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G5125679948
OpenAlex ID: W7212068611