OpenAI · 205-01 · 2026-09-24 · Algebra
Universal Tensor Squares for Symmetric Groups
preprints/Universal-Tensor-Squares-for-Symmetric-Groups-September-24-2026
Family 205. Saxl's conjecture and universal tensor squares.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Proves Saxl's conjecture: the tensor square of every staircase representation contains every irreducible complex representation of the corresponding symmetric group. More generally, every with has an irreducible representation whose tensor square contains all irreducibles.
For every positive integer n other than 2, 4, and 9, we prove that some irreducible complex representation of Sn has a tensor square containing every irreducible representation. This resolves the tensor square conjecture for symmetric groups affirmatively.
Preprint source and Lean scope
The abstract above is the catalogue abstract. The sections below are the full preprint source, 0 sections. This page is not only the abstract. The manuscript file is loading.
This preprint is named in the Lean scope note for 205: Saxl’s conjecture and universal tensor squares. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.