A Stability Property for Coefficients in Kronecker Products of Complex $S_n$ Characters
نویسندگان
چکیده
منابع مشابه
A Stability Property for Coefficients in Kronecker Products of Complex Sn Characters
In this note we make explicit a stability property for Kronecker coefficients that is implicit in a theorem of Y. Dvir. Even in the simplest nontrivial case this property was overlooked despite of the work of several authors. As applications we give a new vanishing result and a new formula for some Kronecker coefficients.
متن کاملGeneralized Stability of Kronecker Coefficients
Kronecker coefficients are tensor product multiplicities for the irreducible representations of the symmetric group. In this paper, we identify directions in the parameter space for tensor products along which these multiplicities are monotone convergent, generalizing a classical result of Murnaghan.
متن کاملAppendix to: Generalized Stability of Kronecker Coefficients
as gl(V1)⊕ gl(V2)⊕ gl(V3)-modules. This yields a well-known reformulation of (2.1). Proposition A.1. If l(α) 6 dimV1 and l(β) 6 dimV2, then the Kronecker coefficient g(αβγ) is the multiplicity of V1(α)⊗ V2(β) in the gl(V1)⊕ gl(V2)-module (V1 ⊗ V2)(γ). If V is m-dimensional, then V (1) is the one-dimensional gl(V )-module carried by the trace map gl(V ) → C. It follows easily that V (n) ∼= V (1)...
متن کاملStability of Kronecker Products of Irreducible Characters of the Symmetric Group
F. Murnaghan observed a long time ago that the computation of the decompositon of the Kronecker product χ(n−a,λ2,... ) ⊗ χ(n−b,μ2,... ) of two irreducible characters of the symmetric group into irreducibles depends only on λ = (λ2, . . . ) and μ = (μ2, . . . ), but not on n. In this note we prove a similar result: given three partitions λ, μ, ν of n we obtain a lower bound on n, depending on λ,...
متن کاملKronecker Products, Characters, Partitions, and the Tensor Square Conjectures
We study the remarkable Saxl conjecture which states that tensor squares of certain irreducible representations of the symmetric groups Sn contain all irreducibles as their constituents. Our main result is that they contain representations corresponding to hooks and two row Young diagrams. For that, we develop a new sufficient condition for the positivity of Kronecker coefficients in terms of c...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2009
ISSN: 1077-8926
DOI: 10.37236/260