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arXiv · 1710.00528

Plethysm and fast matrix multiplication

Tim Seynnaeve
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Abstract

Motivated by the symmetric version of matrix multiplication we study the plethysm $S^k(\mathfrak{sl}_n)$ of the adjoint representation $\mathfrak{sl}_n$ of the Lie group $SL_n$. In particular, we describe the decomposition of this representation into irreducible components for $k=3$, and find highest weight vectors for all irreducible components. Relations to fast matrix multiplication, in particular the Coppersmith-Winograd tensor are presented.

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Tim Seynnaeve. 2017-10-02. Plethysm and fast matrix multiplication. https://doi.org/10.1016/j.crma.2017.11.012

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