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arXiv · 2610.22162

The invariant cell number property for $\mathbb{E}_4$-rings

Anish Chedalavada·Florian Riedel
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Abstract

For any non-zero $\mathbb{E}_4$-ring $R$, we prove that an $n$-fold direct sum of suspensions of $R$ cannot admit an exhaustive filtration by fewer than $n$ cells. We do this by showing that certain integral representations of the symmetric group lift to Schur functors on additively $\mathbb{E}_3$-monoidal $\infty$-categories. We then reduce the statement to a vanishing fact for rational Schur functors due to Deligne.

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Anish Chedalavada, Florian Riedel. 2026-10-15. The invariant cell number property for $\mathbb{E}_4$-rings. https://arxiv.org/abs/2610.22162

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