Preprint 67/2017

Plethysm and fast matrix multiplication

Tim Seynnaeve

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Submission date: 05. Oct. 2017 (revised version: November 2017)
Pages: 7
published in: Comptes rendus mathematique, 356 (2018) 1, p. 52-55 
DOI number (of the published article): 10.1016/j.crma.2017.11.012
MSC-Numbers: 20G05, 68Q17, 15A69
Keywords and phrases: representation theory, Computational complexity
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Link to arXiv: See the arXiv entry of this preprint.

Motivated by the symmetric version of matrix multiplication we study the plethysm Sk(𝔰𝔩n) of the adjoint representation 𝔰𝔩n of the Lie group SLn. 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.

24.11.2021, 02:19