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

Author

Bruce Westbury, Jul 24 2010

Keywords

• nonn
• more

Comments

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

Examples

			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.
		

Links

• 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.