# What is the spinor representation of other groups beside $SO(p, q)$?

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?

• Perhaps it means projective representations? – Seth Whitsitt Oct 19 '19 at 20:36
• @ Seth Whitsitt i am thankful to you if you explain more about it. – Arian Oct 19 '19 at 21:30
• You should cite the paper so I can check to make sure my guess is correct before I write an answer. – Seth Whitsitt Oct 19 '19 at 21:35
• @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. – Arian Oct 20 '19 at 6:58
• 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. – AccidentalFourierTransform Nov 9 '19 at 14:21