ALGEBRAIC COMBINATORICS

no. 2
A tensor-cube version of the Saxl conjecture
Harman, Nate1; Ryba, Christopher2
1 Department of Mathematics University of Michigan Ann Arbor MI 48101 (USA)
2 Department of Mathematics University of California, Berkeley Berkeley CA 94720 (USA)
Algebraic Combinatorics, Volume 6 (2023) no. 2, pp. 507-511.

Let n be a positive integer, and let ρ n =(n,n-1,n-2,...,1) be the “staircase” partition of size N=n+1 2. The Saxl conjecture asserts that every irreducible representation S λ of the symmetric group S N appears as a subrepresentation of the tensor square S ρ n ⊗S ρ n . In this short note we give two proofs that every irreducible representation of S N appears in the tensor cube S ρ n ⊗S ρ n ⊗S ρ n .

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.267
Classification: 20C30
Keywords: Saxl conjecture, symmetric groups
Harman, Nate 1; Ryba, Christopher 2

1 Department of Mathematics University of Michigan Ann Arbor MI 48101 (USA)
2 Department of Mathematics University of California, Berkeley Berkeley CA 94720 (USA)
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Harman, Nate; Ryba, Christopher. A tensor-cube version of the Saxl conjecture. Algebraic Combinatorics, Volume 6 (2023) no. 2, pp. 507-511. doi : 10.5802/alco.267. https://alco.centre-mersenne.org/articles/10.5802/alco.267/

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