{"id":"hexagon/2610.00566","pdf":"https://hexagonmath.org/pdf/2610.00566v1","url":"https://hexagonmath.org/abs/2610.00566v1","tags":["msc:18M30","msc:18M05","Deligne interpolation","Tensor categories","deformations"],"score":0,"title":"Deformations of Deligne's S_t","domain":"math.QA","origin":"ai-generated","source":"hexagon","authors":["Noah Snyder"],"reviews":0,"subject":"math.QA","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus"],"discussed":0,"published":"2026-10-26","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}