The hyperdeterminant of 3 x 3 x 2 arrays, and the simplest invariant of 4 x 4 x 2 arrays

Details The hyperdeterminant of 3 x 3 x 2 arrays, and the simplest invariant of 4 x 4 x 2 arrays The hyperdeterminant of 3 x 3 x 2 arrays, and the simplest invariant of 4 x 4 x 2 arrays

2011-11-25

arxiv.org/abs/1111.6120v1

Mathematics

Representation Theory

15 pages

Scientific paper

We use the representation theory of Lie algebras and computational linear algebra to obtain an explicit formula for the hyperdeterminant of a $3 \times 3 \times 2$ 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 $(S_3 \times S_3 \times S_2) \rtimes S_2$. We also obtain the simplest invariant for a $4 \times 4 \times 2$ 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 $(S_4 \times S_4 \times S_2) \rtimes S_2$.

Affiliated with

Also associated with

No associations

Rating

The hyperdeterminant of 3 x 3 x 2 arrays, and the simplest invariant of 4 x 4 x 2 arrays does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The hyperdeterminant of 3 x 3 x 2 arrays, and the simplest invariant of 4 x 4 x 2 arrays, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The hyperdeterminant of 3 x 3 x 2 arrays, and the simplest invariant of 4 x 4 x 2 arrays will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-483290