The Saxl conjecture and the dominance order

In 2012 Jan Saxl conjectured that all irreducible representations of the symmetric group occur in the decomposition of the tensor square of the irreducible representation corresponding to the staircase partition. We make progress on this conjecture by proving the occurrence of all those irreducibles...

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Bibliographic Details
Published in:Discrete mathematics 2015-11, Vol.338 (11), p.1970-1975
Main Author: Ikenmeyer, Christian
Format: Article
Language:English
Subjects:
Irreducible representations
Kronecker coefficients
Saxl conjecture
Symmetric group
Tensor square conjecture
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Summary:In 2012 Jan Saxl conjectured that all irreducible representations of the symmetric group occur in the decomposition of the tensor square of the irreducible representation corresponding to the staircase partition. We make progress on this conjecture by proving the occurrence of all those irreducibles which correspond to partitions that are comparable to the staircase partition in the dominance order. Moreover, we use our result to show the occurrence of all irreducibles corresponding to hook partitions. This generalizes results by Pak et al. (2013).
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2015.04.027