Using a recursion formula due to Dvir, we obtain information on maximal and almost maximal components in Kronecker products of characters of the symmetric groups. This is applied to confirm a conjecture made by Bessenrodt and Kleshchev in 1999, which classifies all such Kronecker products with only three or four components.

Three properties of matrices: the spark, the mutual incoherence and the restricted isometry property have recently been introduced in the context of compressed sensing. We study these properties for matrices that are Kronecker products and show how these properties relate to those of the factors. For the mutual incoherence we also discuss results for sums of Kronecker products.

Confirming a conjecture made by Bessenrodt and Kleshchev in 1999, we classify all Kronecker products of characters of the symmetric groups with only three or four components. On the way towards this result, we obtain new information about constituents in Kronecker products.

Three properties of matrices: the spark, the mutual incoherence and the restricted isometry property have recently been introduced in the context of compressed sensing. We study these properties for matrices that are Kronecker products and show how these properties relate to those of the factors. For the mutual incoherence we also discuss results for sums of Kronecker products.

Kronecker or inner tensor products of representations of symmetric groups (and many other groups) have been studied for a long time. But even for the symmetric groups no reasonable formula for decomposing Kronecker products of two irreducible complex representations into irreducible components is available (cf. [7, 5]). An equivalent problem is to decompose the inner product of the correspondin...