Geometric Aspects of Iterated Matrix Multiplication

Abstract

This paper studies geometric properties of the Iterated Matrix Multiplication polynomial and the hypersurface that it defines. We focus on geometric aspects that may be relevant for complexity theory such as the symmetry group of the polynomial, the dual variety and the Jacobian loci of the hypersurface, that are computed with the aid of representation theory of quivers.

20 pages - minor typos have been fixed - final version to appear in Journal of Algebra

References in corpus (3)

• An introduction to geometric complexity theory
• Explicit Lower Bounds via Geometric Complexity Theory
• Lectures on the geometry of flag varieties

Cited by in corpus (6)

• Dimension of Tensor Network varieties
• Matrix product states and the quantum max-flow/min-cut conjectures
• The geometry of rank decompositions of matrix multiplication I: 2x2 matrices
• The geometry of rank decompositions of matrix multiplication II: $3\times 3$ matrices
• On algebraic branching programs of small width
• Geometric complexity theory and matrix powering