Plane Partitions and Characters of the Symmetric Group
نویسنده
چکیده
In this paper we show that the existence of plane partitions, which are minimal in a sense to be defined, yields minimal irreducible summands in the Kronecker product χ ⊗ χ of two irreducible characters of the symmetric group S(n). The minimality of the summands refers to the dominance order of partitions of n. The multiplicity of a minimal summand χ equals the number of pairs of Littlewood-Richardson multitableaux of shape (λ, μ), conjugate content and type ν. We also give lower and upper bounds for these numbers.
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