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Saxl Conjecture


Saxl's conjecture asserts that the tensor square of the complex Specht module indexed by the staircase partition

 rho_m=(m,m-1,...,1)

contains every irreducible representation of S_N, where N=m(m+1)/2. It is equivalently the requirement g(rho_m,rho_m,nu)>0 for every partition nu of N. The staircase is self-conjugate, as required for the sign representation to occur in the square.


See also

Kronecker Coefficient, Specht Module, Symmetric Group, Tensor Square Conjecture

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References

Pak, I.; Panova, G.; and Vallejo, E. "Kronecker Products, Characters, Partitions, and the Tensor Square Conjectures." Adv. Math. 288, 702-731, 2016. https://doi.org/10.1016/j.aim.2015.11.002.Sagan, B. E. The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions, 2nd ed. New York: Springer, 2001. https://doi.org/10.1007/978-1-4757-6804-6.

Cite this as:

Weisstein, Eric W. "Saxl Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SaxlConjecture.html

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