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MiS Preprint

Plethysm and fast matrix multiplication

Tim Seynnaeve


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.

MSC Codes:
20G05, 68Q17, 15A69
representation theory, Computational complexity

Related publications

2018 Repository Open Access
Tim Seynnaeve

Plethysm and fast matrix multiplication

In: Comptes rendus mathematique, 356 (2018) 1, pp. 52-55