A hyperdeterminant for 2 x 2 x 3 arrays

Details A hyperdeterminant for 2 x 2 x 3 arrays A hyperdeterminant for 2 x 2 x 3 arrays

2011-06-15

arxiv.org/abs/1106.2988v1

Mathematics

Representation Theory

11 pages

Scientific paper

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.

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