Deformations of Deligne's S_t
Snyder and Spencer showed that every *ribbon* infinitesimal deformation of the trivalent category $\mathcal{S}_t$ underlying Deligne's $\mathrm{Rep}(S_t)$ comes from varying $t$. Here we remove the braided hypothesis: every pivotal deformation of $\mathcal{S}_t$, $t\neq0$, over a local Artinian $\mathbb{C}$-algebra comes from varying $t$. The pivotal hypothesis turns out to be automatic, so the same holds for monoidal deformations. Since $\mathcal{S}_t$ is not generated as a pivotal category by its trivalent vertex, the crossing must be added as a generator, and the Reidemeister moves only…
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