Pseudorepresentations not arising from genuine representations

2023/10/25 by Jinyue Luo, Luo, Jinyue · 1 citation
Mathematics · #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2310.16953

Abstract

We show that a pseudorepresentation D\colon A[G] → A of a (finite) group G need not arise from a genuine representation, even if one is allowed to extend the ring A. This shows that a theorem of the "embedding problem" for residually multiplicity free pseudorepresentations can not be extended to the general setting.

Citations

• Caractérisation des caractères et Pseudo-caractères
• On ordinary ?-adic representations associated to modular forms
• A formal inverse to the Cayley-Hamilton theorem
• The invariant theory of n × n matrices
• Finite dimensional representations of algebras

Cited by

• Deformations of pseudocharacters and Mazur's finiteness condition

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• Deformations of pseudocharacters and Mazur's finiteness condition