A179685 The dimension of the space of invariant tensors in the n-th tensor power of the adjoint representation of the exceptional Lie algebra F4.

1, 0, 1, 1, 5, 16, 80, 436, 2891, 22248, 198774, 2029140, 23310386, 296407466, 4109654354, 61348443380, 976111067870, 16423368282336, 290404344321126, 5370042566624118, 103427555919931446

Offset

0,5

Comments

This is known to satisfy a linear recurrence relation with polynomial coefficients. The limit of a(n+1)/a(n) is 52.

Links

Table of n, a(n) for n=0..20.

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

Scott Morrison, Noah Snyder, and Dylan P. Thurston, Towards the quantum exceptional series, arXiv:2402.03637 [math.QA], 2024. See p. 38.

Example

The n-th tensor power is the trivial representation for n=0 and is the adjoint representation for n=1. For n=2 every invariant tensor is a scalar multiple of a Killing form.

Crossrefs

Sequence in context: A372174 A227292 A179683 * A286077 A286072 A002830

Adjacent sequences: A179682 A179683 A179684 * A179686 A179687 A179688

Keyword

nonn,more,changed

Author

Bruce Westbury, Jul 24 2010

Status

approved