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

0,5

Comments

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

Links

Bruce Westbury, Table of n, a(n) for n = 0..30

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: A197052 A334647 A203852 * A372174 A227292 A179683

Adjacent sequences: A179660 A179661 A179662 * A179664 A179665 A179666

Keyword

nonn

Author

Bruce Westbury, Jul 23 2010

Status

approved