Saxl’s conjecture and universal tensor squares

What OpenAI claims

Proves Saxl's conjecture: the tensor square of every staircase representation contains every irreducible complex representation of the corresponding symmetric group. More generally, every Sn with n ∉ {2,4,9} has an irreducible representation whose tensor square contains all irreducibles. (Lean)

Papers (2)

1. Universal Tensor Squares for Symmetric Groups

   24 September 2026 · Preprint, not peer reviewed · PDF

   OpenAI's abstract 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.

2. A Cyclic Polytabloid Proof of Saxl's Conjecture

   24 September 2026 · Preprint, not peer reviewed · PDF

   OpenAI's abstract For every staircase partition, we prove that the tensor square of the corresponding irreducible complex representation of the symmetric group contains every irreducible representation of that group. This proves Saxl's conjecture.

Status

Preprint. The papers have not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.