• A Geometric Approach to the Kronecker Problem I: The Two Row Case

• Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/118/02/0213-0226

• Keywords

Kronecker product; symmetric group representations; geometric complexity.

• Abstract

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.

• Author Affiliations

1. Chennai Mathematical Institute, Plot H1, SIPCOT IT Park, Padur P.O., Siruseri 603 103, India

• Proceedings – Mathematical Sciences

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Volume 129 | Issue 3
June 2019