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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
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
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
KEYWORD
nonn
AUTHOR
Bruce Westbury, Jul 24 2010
STATUS
approved