Aarhus University Seal / Aarhus Universitets segl

Horn inequalities for nonzero Kronecker coefficients

Nicolas Ressayre
(Institut Camille Jordan)
Tirsdag, 18 september, 2012, at 16:15-17:15, in Aud. D3 (1531-215)
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 decompositions of  the tensor products of two irreducible representations of symmetric groups (resp. linear groups). By a classical Littlewood-Murnaghan's result the Kronecker coefficients generalize the Littlewood-Richardson ones. The nonvanishing of some Littlewood-Richardson coefficient $c_{\alpha\beta}^\gamma$ implies that $(\alpha, \beta, \gamma)$ satisfies some linear inequalities called Horn inequalities. In this talk, we extend some Horn inequalities (precisely the essential ones) to the triples of partitions corresponding to a nonzero Kronecker coefficient.