2011/11/25 by Murray R. Bremner, Bremner, Murray R.
Biochemistry, Genetics and Molecular Biology · Mathematics · #14-3-3 protein interactions #15A69 #17B10 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.AG #math.RT #msc:15A69 #msc:17B10
paper · pdf · doi:10.48550/arxiv.1111.6120
15 pages
arxiv created 2011/11/25 · openalex publication_date 2011/11/25 · arxiv updated 2011/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We use the representation theory of Lie algebras and computational linear algebra to obtain an explicit formula for the hyperdeterminant of a 3 × 3 × 2 array: a homogeneous polynomial of degree 12 in 18 variables with 16749 monomials and 41 distinct integer coefficients; the monomials belong to 178 orbits under the action of (S3 × S3 × S2) \rtimes S2. We also obtain the simplest invariant for a 4 × 4 × 2 array: a homogeneous polynomial of degree 8 in 32 variables with 14148 monomials and 13 distinct integer coefficients; the monomials belong to 28 orbits under (S4 × S4 × S2) \rtimes S2.