A hyperdeterminant for 2 x 2 x 3 arrays
Representation Theory
2011-06-16 v1 High Energy Physics - Theory
Mathematical Physics
math.MP
Rings and Algebras
Abstract
We use the representation theory of Lie algebras and computational linear algebra to determine the simplest nonconstant invariant polynomial in the entries of a general 2 x 2 x 3 array. This polynomial is homogeneous of degree 6 and has 66 terms with coefficients 1, -1, 2, -2 in the 12 indeterminates x_ijk where i,j = 1,2 and k = 1,2,3. This invariant can be regarded as a natural generalization of Cayley's hyperdeterminant for 2 x 2 x 2 arrays.
Cite
@article{arxiv.1106.2988,
title = {A hyperdeterminant for 2 x 2 x 3 arrays},
author = {Murray R. Bremner},
journal= {arXiv preprint arXiv:1106.2988},
year = {2011}
}
Comments
11 pages