Saxl's conjecture: the tensor square of the staircase representation contains every irreducible representation of the symmetric group

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The tensor square conjecture for symmetric groups: some irreducible representation of S_n has a tensor square containing every irreducible evidence for this event

VibeMathed record: Saxl's conjecture: the tensor square of the staircase representation contains every irreducible representation of the symmetric group evidence for this event

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Companion manuscript: A Cyclic Polytabloid Proof of Saxl's Conjecture evidence for this event

Lean proof: OAI/RepresentationTheory/Saxl/Main.lean evidence for this event

Pak, Panova and Vallejo, Kronecker products, characters, partitions, and the tensor square conjectures evidence for this event

Theorem 1.1: for every $m\ge1$ and every $\lambda\vdash N_m=m(m+1)/2$, $g(\rho_m,\rho_m,\lambda)>0$, so the tensor square of the staircase Specht module contains every irreducible representation of $S_{N_m}$. The proof gives the stronger statement that every constituent occurs inside one explicitly generated cyclic submodule of the tensor square, extending Ikenmeyer's triangular arrangement of alternating tensors. Not shown: values or bounds for these Kronecker coefficients, or a combinatorial interpretation of them. parent of this event

Saxl's conjecture: the tensor square of the staircase representation contains every irreducible representation of the symmetric group parent of this event

Lean statement: ComparatorChallenges/Saxl.lean evidence for this event