Geodesic
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, Tome 6 (2023) no. 2, pp. 507-511

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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 .

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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)
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Harman, Nate; Ryba, Christopher. A tensor-cube version of the Saxl conjecture. Algebraic Combinatorics, Tome 6 (2023) no. 2, pp. 507-511. doi: 10.5802/alco.267

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