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arXiv · 2607.23857

Counterexamples to Norm Conjectures of Wehlau in Modular Invariant Theory

Muhammad Fazeel Anwar
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Abstract

Let $G$ be a finite group and let $V$ be a finite-dimensional $G$-module over a field $k$. We construct explicit counterexamples in characteristic $2$ to conjectures of Wehlau concerning norms. We give faithful four-dimensional representations of $C_2^3$ and $C_2^4$ over $\mathbb F_8$ for which every nonlinear orbit norm is decomposable; in the $C_2^4$ example, the invariant ring is polynomial, thereby disproving both Wehlau's norm conjecture and its unrestricted extension.

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BibTeXRIS

Muhammad Fazeel Anwar. 2026-07-26. Counterexamples to Norm Conjectures of Wehlau in Modular Invariant Theory. https://arxiv.org/abs/2607.23857

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