Editing Representation theory of SU(2) (section)

===Relation to the representations of SO(3)===
{{see also|Rotation group SO(3)#Connection between SO(3) and SU(2)|Projective representation}}
Note that either all of the weights of the representation are even (if <math>m</math> is even) or all of the weights are odd (if <math>m</math> is odd). In physical terms, this distinction is important: The representations with even weights correspond to ordinary representations of the [[rotation group SO(3)]].<ref>{{harvnb|Hall|2015}} Section 4.7</ref> By contrast, the representations with odd weights correspond to double-valued (spinorial) representation of SO(3), also known as [[projective representation]]s.

In the physics conventions, <math>m</math> being even corresponds to <math>l</math> being an integer while <math>m</math> being odd corresponds to <math>l</math> being a half-integer. These two cases are described as [[integer spin]] and [[half-integer spin]], respectively. The representations with odd, positive values of <math>m</math> are faithful representations of SU(2), while the representations of SU(2) with non-negative, even <math>m</math> are not faithful.<ref>{{Cite book|url=https://books.google.com/books?id=1jw8DQAAQBAJ|title=Group Theory for Physicists|last=Ma|first=Zhong-Qi|date=2007-11-28|publisher=World Scientific Publishing Company|isbn=9789813101487|pages=120|language=en}}</ref>