{"id":"openai-math/Universal-Tensor-Squares-for-Symmetric-Groups","pdf":"https://github.com/openai/math/blob/main/preprints/Universal-Tensor-Squares-for-Symmetric-Groups-September-24-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Universal-Tensor-Squares-for-Symmetric-Groups-September-24-2026","tags":["representation-theory","symmetric-groups","tensor-squares","group-theory"],"score":0,"title":"Universal Tensor Squares for Symmetric Groups","domain":"Algebra","family":"205","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.RA","summary":"For every positive integer n other than 2, 4, and 9, we prove that some irreducible complex representation of S n has a tensor square containing every irreducible representation. This resolves the tensor square conjecture for symmetric groups affirmatively.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Saxl’s conjecture and universal tensor squares"}