Uniqueness of factorization for fusion-invariant representations

2023/03/18 by José Cantarero, Cantarero, José, Germán Combariza +1 · 1 citation
Engineering · Mathematics · #20D20 (Primary) 20C15 #20M14 (Secondary) #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2303.10341

openalex publication_date 2023/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a saturated fusion system F over a finite p-group S, we provide criteria to determine when uniqueness of factorization into irreducible F--invariant representations holds. We use them to prove uniqueness of factorization when the order of S is at most p³. We also describe an example where the monoid of fusion-invariant representations is not even half-factorial. Finally, we find other examples of fusion systems where this monoid is not factorial using GAP.

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