Projective Unitary Irreducible Representations and Spin

In this section we define irreducible projective representations and find the irreducible projective representations of 50(3). These turn out to correspond to the different kinds of spin elementary particles can have, namely, 0, 1/2, 1, 3/2. 

We start by defining the projective unitary representations. Recall the unitary group ZT (V) of a complex scalar product space V from Definition 4.2. The following definition is an analog of Definition 4.11. 

Definition 10.6 Suppose V is a complex scalar product space. projective unitary group of V is 

First we must check that the multiplication on U (V) descends to the 

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