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Let $G$ be a Lie group. The set of all $N$ such that $G$ is a subgroup of $SO(N)$ has a minimum $N_{\min}(G)$. (If I am not wrong, $N_{\min}(G)$ is supposed to be less or equal to $\dim(G)$)

What is the value of $N_{\min}(G)$, with $G$ = (compact real forms) $E_6, E_7, E_8, E_6\times E_6, E_7\times E_7, E_8\times E_8$ ?

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    Do you mean $E_6$, $E_7$, $E_8$, $E_6 \times E_6$, $E_7 \times E_7$, $E_8 \times E_8$?2012-01-03
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    Isn't it the other way around: $N_\min(G) \geq \dim{(G)}$ (for dimension reasons, for example)? If $G$ is non-compact then $N_\min{(G)}$ can well be infinite.2012-01-03
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    Zhen Lin : Yes t.b : Yes, maybe, but exceptionnal Lie groups are compact, no ?.2012-01-03
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    When you write $E_6$ and so on, *what* group do you have in mind? That only identifies the Lie algebra.2012-01-04
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    @Mariano Suárez-Alvarez These are the compact real form. I am going to edit this.2012-01-05

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