Articles written in Proceedings – Mathematical Sciences
Volume 118 Issue 2 May 2008 pp 213-226 Research Articles
Given two irreducible representations $\mu,\upsilon$ of the symmetric group $S_d$, the Kronecker problem is to find an explicit rule, giving the multiplicity of an irreducible representation, 𝜆, of $S_d$, in the tensor product of 𝜇 and 𝜐. We propose a geometric approach to investigate this problem. We demonstrate its effectiveness by obtaining explicit formulas for the tensor product multiplicities, when the irreducible representations are parameterized by partitions with at most two rows.