Plane Partitions and Characters of the Symmetric Group.

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^λ ⊗ χ^μ 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^ν 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. [ABSTRACT FROM AUTHOR]