Editing Projective representation (section)

===Projective representations of SO(3)===
A physically important example of the above construction comes from the case of the [[rotation group SO(3)]], whose [[Rotation group SO(3)#Connection between SO(3) and SU(2)|universal cover is SU(2)]]. According to the [[representation theory of SU(2)]], there is exactly one irreducible representation of SU(2) in each dimension. When the dimension is odd (the "integer spin" case), the representation descends to an ordinary representation of SO(3).<ref>{{harvnb|Hall|2015}} Section 4.7</ref> When the dimension is even (the "fractional spin" case), the representation does not descend to an ordinary representation of SO(3) but does (by the result discussed above) descend to a projective representation of SO(3). Such projective representations of SO(3) (the ones that do not come from ordinary representations) are referred to as "spinorial representations", whose elements (vectors) are called [[spinors]].

By an argument discussed below, every finite-dimensional, irreducible ''projective'' representation of SO(3) comes from a finite-dimensional, irreducible ''ordinary'' representation of SU(2).