# Spinors in more dimensions and new degeneracies?

As you more than probably know spinors dimensions go as $2^{\frac{D}2}$ in D spacetime dimensions. If we look at the peculiar case of D=2*4, spinors have 4 components and we usually say that's related to the 4 "degrees of freedom": particle/antiparticule & spin up/down?*. So basically linked to the degeneracy in energy and spin. But if we know go to D=6, they have 8 components, I am asking myself if it's not the appearance of a new physical degeneracy, but I don't really see what could it be. Maybe the group of rotation in 6 dimension has one more Casimir operator. Am I seeing it in a totally wrong way?

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