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Results tagged with exceptional-groups
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user 484566
Exceptional Lie groups G2, F4, E6, E7, E8 of dimensions 14, 52, 78, 133, 248 were obtained as result of classification of simple Lie groups performed by Killing and Elie Cartan. The tool used in classification is Dynkin diagram and root system of vectors in Lie algebra of the group. The remaining Lie groups form four infinite families of transformations of n-dimensional space over real (odd and even), complex and quaternionic field.
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Why do these two irreps of $E_6$ have the same dimension?
$\newcommand\Sym{\mathrm{Sym}}$
An extended comment which more or less suggests that your suggested answer might be as good as one can do.
If $G$ has a representation on $V$ which preserves a symmetri …
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