Counterexamples to Norm Conjectures of Wehlau in Modular Invariant Theory

2026/07/26 by Muhammad Fazeel Anwar
#math.RT #math.AC #math.RA

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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 C₂³ and C₂⁴ over \mathbb F₈ for which every nonlinear orbit norm is decomposable; in the C₂⁴ example, the invariant ring is polynomial, thereby disproving both Wehlau's norm conjecture and its unrestricted extension.

Citations

• Rings of invariants for modular representations of elementary abelian p-groups

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