Talks
Fall 2014

# Inequalities and Reductions for Nonzero Kronecker Coefficients

Tuesday, September 16th, 2014 1:20 pm2:10 pm

The Kronecker coefficients $g_{\alpha\beta\gamma}$ and the Littlewood-Richardson coefficients $c_{\alpha\beta}^\gamma$ are nonnegative integers depending on three partitions $\alpha$, $\beta$, and $\gamma$. By definition, $g_{\alpha\beta\gamma}$ (resp. $c_{\alpha\beta}^\gamma$) are the multiplicities of the tensor product decomposition of two irreducible representations of symmetric groups (resp. linear groups). By a classical Littlewood-Murnaghan's result the Kronecker coefficients extend the Littlewood-Richardson ones.
The nonvanishing of the Littlewood-Richardson coefficient $c_{\alpha\beta}^\gamma$ implies that $(\alpha, \beta, \gamma)$ satisfies some linear inequalities called Horn inequalities. We extend some Horn inequalities to the triples of partitions corresponding to a nonzero Kronecker coefficient.