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Saxl’s conjecture and universal tensor squares
Proves Saxl's conjecture: the tensor square of every staircase representation contains every irreducible complex representation of the corresponding symmetric group. More generally, every S with has an irreducible representation whose tensor square contains all irreducibles.
Manuscripts in this family · 2
Universal Tensor Squares for Symmetric Groups
Sep 24, 2026·main.pdf
For every positive integer n other than 2, 4, and 9, we prove that some irreducible complex representation of S has a tensor square containing every irreducible representation. This resolves the tensor square conjecture for symmetric groups affirmatively.
A Cyclic Polytabloid Proof of Saxl's Conjecture
Sep 24, 2026·paper.pdfLean
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.