The Saxl conjecture for fourth powers via the semigroup property
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Author(s)
Luo, Sammy Y.
Sellke, Mark A.
Date Issued
August 2016
Journal
Journal of Algebraic Combinatorics
Publisher
Springer US
Citation
Luo, Sammy, and Mark Sellke. “The Saxl Conjecture for Fourth Powers via the Semigroup Property.” Journal of Algebraic Combinatorics 45.1 (2017): 33–80.
Version
Author's final manuscript
Abstract
The tensor square conjecture states that for n ≥ 10, there is an irreducible representation V of the symmetric group Sn such that V⊗V contains every irreducible representation of S[subscript n]. Our main result is that for large enough n, there exists an irreducible representation V such that V[superscript ⊗4] contains every irreducible representation. We also show that tensor squares of certain irreducible representations contain (1−o(1))-fraction of irreducible representations with respect to two natural probability distributions. Our main tool is the semigroup property, which allows us to break partitions down into smaller ones.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s10801-016-0700-z
