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Let $G$ be a connected compact simple Lie group of one of the following types: $A_l$, $B_l$, $C_l$, $D_l$, $E_6$, $E_7$, $E_8$, $F_4$, $G_2$. Which one of these admit an irreducible faithful representation?

Links that might help:

https://mathoverflow.net/questions/328138/non-faithful-irreducible-representations-of-simple-lie-groups?rq=1;

Lowest-dimensional faithful representations of compact Lie groups

Emanuele
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  • This is again the discussion here, right? You are not referring to the simply connected group, aren't you? – Dietrich Burde Jun 03 '20 at 13:09
  • Isn't it so that (barring the trivial rep) an irreducible rep is faithful if its injective on the center of $G$? This leads to excluding certain highest weights. The exact set depends on how close to being simply connected $G$ is. In other words, the MathOverflow thread gives the answer. – Jyrki Lahtonen Jun 03 '20 at 13:10
  • Yes it is the same discussion, since one year ago I did not get a precise answer. We may ask eventually $G$ to be simply-connected yes. – Emanuele Jun 03 '20 at 13:22

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