A353173 Dimension of space of invariants of n-th tensor power of the 26-dimensional fundamental (or "standard") irreducible representation of F_4.
1, 0, 1, 1, 5, 15, 70, 330, 1820, 10858, 70875, 497135, 3727955, 29658410, 248989676, 2194891440, 20231692430, 194286848280, 1937546532820, 20008993160460, 213436182918652, 2346406693816315, 26531060178217182, 307987244037724262, 3664579007885995952
Offset: 0
Keywords
Examples
a(1)=0 because there is no F_4-invariant linear form on the 26-dimensional representation; a(2)=1 because there is, up to scalars, precisely one invariant quadratic form.
Links
Crossrefs
The analogous sequence for the (52-dimensional) adjoint representation of F_4 is: A179685.
A similar sequence for G_2 (for its 7-dimensional fundamental irreducible representation) is: A059710.
A similar sequence for B_2 (for its standard 5-dimensional irreducible representation) is: A095922.
For A_n the similar sequence (omitting some 0's) is given by the (n+1)-dimensional Catalan numbers, e.g., A005789 for A_2.
Programs
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LiE
p_tensor(n,[0,0,0,1],F4)|[0,0,0,0] # Returns the value of a(n).
Comments