OpenAI research collection · 2 manuscripts · Source checked 2026-10-19
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_(n) with n\notin\{2,4,9\} has an irreducible representation whose tensor square contains all irreducibles.
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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.
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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.
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