Plethysm and fast matrix multiplication

10/02/2017

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by   Tim Seynnaeve, et al.

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Motivated by the symmetric version of matrix multiplication we study the plethysm S^k(sl_n) of the adjoint representation 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.