Deligne categories and reduced Kronecker coefficients
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10801_2016_Article_672.pdf
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Author(s)
Entova-Aizenbud, Inna
Date Issued
February 2016
Journal
Journal of Algebraic Combinatorics
Publisher
Springer US
Citation
Entova Aizenbud, Inna. “Deligne Categories and Reduced Kronecker Coefficients.” Journal of Algebraic Combinatorics 44.2 (2016): 345–362.
Version
Author's final manuscript
Abstract
The Kronecker coefficients are the structural constants for the tensor categories of representations of the symmetric groups, namely, given three partitions λ,μ,τ of n, the multiplicity of λ in μ⊗τ is called the Kronecker coefficient g[superscript λ][subscript μ,τ]. When the first part of each of the partitions is taken to be very large (the remaining parts being fixed), the values of the appropriate Kronecker coefficients stabilize; the stable value is called the reduced (or stable) Kronecker coefficient. These coefficients also generalize the Littlewood–Richardson coefficients and have been studied quite extensively. In this paper, we show that reduced Kronecker coefficients appear naturally as structure constants of Deligne categories [bar under Rep](S[subscript t]). This allows us to interpret various properties of the reduced Kronecker coefficients as categorical properties of Deligne categories [bar under Rep](S[subscript t]) and derive new combinatorial identities.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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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/s10801-016-0672-z
