Deligne categories and reduced Kronecker coefficients

2014/07/06 by Inna Entova-Aizenbud, Entova-Aizenbud, Inna
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1407.1506

openalex publication_date 2014/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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^λ_{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 the Deligne categories \underlineRep(S_t). This allows us to interpret various properties of the reduced Kronecker coefficients as categorical properties of the categories \underlineRep(S_t).

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