Plethysm and fast matrix multiplication

Tim Seynnaeve

Contact the author: Please use for correspondence this email.
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
Bibtex
MSC-Numbers: 20G05, 68Q17, 15A69
Keywords and phrases: representation theory, Computational complexity
Download full preprint: PDF (278 kB)
Link to arXiv: See the arXiv entry of this preprint.

Abstract:
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.