A179663 The dimension of the space of invariant tensors in the n-th tensor power of the adjoint representation of the exceptional Lie algebra E8.

1, 0, 1, 1, 5, 16, 79, 421, 2674, 19244, 156612, 1423028, 14320350, 158390872, 1912977222, 25083283995, 355246037162, 5409471180024, 88200546561838, 1534120589972637, 28369229081383675, 556021169447494656, 11517512836906556032, 251487262264563372960

Offset: 0

Author

Bruce Westbury, Jul 23 2010

Keywords

• nonn

Comments

This is known to satisfy a linear recurrence relation with polynomial coefficients. The limit of a[n+1]/a[n] is 248.

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

• Bruce Westbury, Table of n, a(n) for n = 0..30
• Jacob L. Bourjaily, Michael Plesser, and Cristian Vergu, The Many Colours of Amplitudes, arXiv:2412.21189 [hep-th], 2024. See p. 53.