Plethysm and fast matrix multiplication
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Submission date: 05. Oct. 2017 (revised version: November 2017)
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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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.