A179684 The dimension of the space of invariant tensors in the n-th tensor power of the adjoint representation of the exceptional Lie algebra E6.

1, 0, 1, 1, 5, 17, 90, 542, 3962, 33554, 324489, 3520885, 42300709, 556530474, 7945317484, 122145525208, 2008827010000, 35143981009968

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 78.

Links

Table of n, a(n) for n=0..17.

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

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: A212291 A307176 A309175 * A250744 A197875 A203116

Adjacent sequences: A179681 A179682 A179683 * A179685 A179686 A179687

Keyword

nonn,more,changed

Author

Bruce Westbury, Jul 24 2010

Status

approved