Plethysm and fast matrix multiplication

Abstract

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 $S{L}_n$. 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.

5 pages

References in corpus (3)

• Secants of minuscule and cominuscule minimal orbits
• Plethysm and lattice point counting
• On the geometry of border rank algorithms for matrix multiplication and other tensors with symmetry

Cited by in corpus (1)

• Bounds on complexity of matrix multiplication away from CW tensors