A tensor-cube version of the Saxl conjecture

tition of size N = ( n+1 ABSTRACT Let n be a positive integer, and let rho n = ( n, n -1 , n -2 , ... , 1) be the "staircase" par) . The Saxl conjecture asserts that every irreducible representation S lambda 2 of the symmetric group S N appears as a subrepresentation of the tensor square S rho A (R) S rho A . In this short note we give two proofs that every irreducible representation of S N appears in the tensor cube S rho A (R) S rho A (R) S rho A .