Abstract
For a prime p, we show that uniqueness of factorization into irreducible \(\Sigma _{p^2}\)-invariant representations of \({\mathbb Z}/p \wr {\mathbb Z}/p\) holds if and only if \(p=2\). We also show nonuniqueness of factorization for \(\Sigma _8\)-invariant representations of \(D_8 \wr {\mathbb Z}/2\). The representation ring of \(\Sigma _{p^2}\)-invariant representations of \({\mathbb Z}/p \wr {\mathbb Z}/p\) is determined completely when p equals two or three.
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Acknowledgements
Project supported by Consejo Nacional de Humanidades, Ciencias y Tecnologías (CONAHCYT) in the year 2023 under Frontier Science Grant CF-2023-I-2649. We thank the anonymous referee/s for their feedback.
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Appendix A. Character Tables
Appendix A. Character Tables
In this appendix, we show the character tables of \({\mathbb Z}/3 \wr {\mathbb Z}/3\) and \(D_8 \wr {\mathbb Z}/2\) following the notations of Sect. 4 and Sect. 6 (Tables 6 and 7).
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Cantarero, J., Gaspar-Lara, J. Fusion-Invariant Representations for Symmetric Groups. Bull. Iran. Math. Soc. 50, 29 (2024). https://doi.org/10.1007/s41980-024-00867-y
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DOI: https://doi.org/10.1007/s41980-024-00867-y