Tensor Powers of Indecomposable Modules for $F\mathfrak{S}_p$

Manzu Kua; Kay Jin Lim

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arXiv · 2607.16626

Tensor Powers of Indecomposable Modules for $F\mathfrak{S}_p$

Manzu Kua·Kay Jin Lim

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Abstract

In the earlier paper arXiv:2603.11533, the authors gave an explicit tensor product formula, modulo projectives, for modules over the group algebra $F\mathfrak{S}_p$. In this paper, we use this formula to study tensor powers of such modules. In certain cases, we give combinatorial descriptions of the multiplicities of the indecomposable summands appearing in their direct-sum decompositions. We also study the asymptotic behaviour of these multiplicities as the underlying prime tends to infinity.

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BibTeX RIS

Manzu Kua, Kay Jin Lim. 2026-07-18. Tensor Powers of Indecomposable Modules for $F\mathfrak{S}_p$. https://arxiv.org/abs/2607.16626

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