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A179663
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The dimension of the space of invariant tensors in the n-th tensor power of the adjoint representation of the exceptional Lie algebra E8.
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0
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1, 0, 1, 1, 5, 16, 79, 421, 2674, 19244, 156612, 1423028, 14320350, 158390872, 1912977222, 25083283995, 355246037162, 5409471180024, 88200546561838, 1534120589972637
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OFFSET
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0,5
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COMMENTS
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This is known to satisfy a linear recurrence relation with polynomial coefficients. The limit of a[n+1]/a[n] is 248.
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LINKS
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Table of n, a(n) for n=0..19.
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EXAMPLE
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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.
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CROSSREFS
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Sequence in context: A138550 A197052 A203852 * A179683 A179685 A002830
Adjacent sequences: A179660 A179661 A179662 * A179664 A179665 A179666
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KEYWORD
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nonn
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AUTHOR
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Bruce Westbury (Bruce.Westbury(AT)warwick.ac.uk), Jul 23 2010
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STATUS
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approved
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