A227292 Dimension of space of invariant tensors in the n-th tensor power of the adjoint representation of G2.

1, 0, 1, 1, 5, 16, 80, 436, 2786, 19538, 147771, 1182095, 9890463, 85866068, 769212600, 7080642324, 66754295740, 642857161008, 6309892895338, 6300760829973, 639049976047882, 6574281878157350, 68519019810831408, 722711344283052608, 7707346411412142258, 83037096707432139882

Offset

0,5

Comments

The limit a(n+1)/a(n) is 14. This is expected to be D-finite (and P-finite).

Links

Table of n, a(n) for n=0..25.

Jacob L. Bourjaily, Michael Plesser, and Cristian Vergu, The Many Colours of Amplitudes, arXiv:2412.21189 [hep-th], 2024. See p. 53.

Example

For n=0 we have the trivial representation for n=2 we have the Killing form.

Prog

(LiE) p_tensor(n, [0, 1], G2)|[0, 0]

Crossrefs

Cf. A002137, A179663, A179683.

Sequence in context: A203852 A179663 A372174 * A179683 A179685 A286077

Adjacent sequences: A227289 A227290 A227291 * A227293 A227294 A227295

Keyword

nonn,changed

Author

Bruce Westbury, Jul 05 2013

Status

approved