Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Chedalavada, Anish, Riedel, Florian
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222579439