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# Jonah Blasiak : Kronecker coefficients for one hook shape

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The Kronecker coefficient $g_{\lambda \mu \nu}$ is the multiplicity of an irreducible $\mathcal{S}_n$-module $M_\nu$ in the tensor product $M_\lambda \otimes M_\mu$. A fundamental open problem in algebraic combinatorics is to find a positive combinatorial formula for these coefficients. We give such a formula in the case that one of the partitions is a hook shape. Our main tool is Haiman's mixed insertion, which is a generalization of Schensted insertion to colored words. Prior familiarity with combinatorics of words and tableaux will not be assumed.

• CategoryColloquium
• Duration: 01:25:14
• Date:  September 25, 2012 at 4:25 PM
• Tags:

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