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A179684
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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 E6.
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0
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1, 0, 1, 1, 5, 17, 90, 542, 3962, 33554, 324489, 3520885, 42300709, 556530474, 7945317484, 122145525208, 2008827010000, 35143981009968
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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 78.
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LINKS
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Table of n, a(n) for n=0..17.
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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: A089923 A145041 A212291 * A197875 A203116 A198090
Adjacent sequences: A179681 A179682 A179683 * A179685 A179686 A179687
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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 24 2010
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STATUS
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approved
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