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I am studying a lecture about superconformal algebras and it claims that there is a superconformal algebra in $d=5$ where supercharges belongs to spinor representation of $F_4$ (which is an exceptional group) as far as I know, spinor representation is a special representation of $SO(p, q)$. what mean when we are talking about spinor representation of other groups?

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    $\begingroup$ Perhaps it means projective representations? $\endgroup$ – Seth Whitsitt Oct 19 '19 at 20:36
  • $\begingroup$ @ Seth Whitsitt i am thankful to you if you explain more about it. $\endgroup$ – Arian Oct 19 '19 at 21:30
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    $\begingroup$ You should cite the paper so I can check to make sure my guess is correct before I write an answer. $\endgroup$ – Seth Whitsitt Oct 19 '19 at 21:35
  • $\begingroup$ @Seth Whitsitt arxiv.org/abs/hep-th/9712074 page 31, sorry it was about G2 group. my question is not about superconformal algebras and i just want to know about spinor representation of other groups. $\endgroup$ – Arian Oct 20 '19 at 6:58
  • $\begingroup$ A spinor is a rep of Spin(n) that does not descend to a rep of SO(n). It has no other accepted meaning. One could extend this definition for general group $G$ to a rep of $\tilde G$ that does not descend to a rep of $G$, with $\tilde G$ the universal cover of $G$. But $G_2$ is simply connected and centerless, so it contains no spinors in this sense. $\endgroup$ – AccidentalFourierTransform Nov 9 '19 at 14:21

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