EDIT: The vector space for the $(\frac{1}{2},0)$ Representation is $\mathbb{C}^2$ as mentioned by Qmechanic in the comments to his answer below! The vector spaces for the other representations remain unanswered.
The definition of a representation is a map (a homomorphism) to the space of linear operators over a vector space. My question is: What are the corresponding vector spaces for the
- $(0,0)$ Representation
- $(\frac{1}{2},0)$ Representation
$(0,\frac{1}{2})$ Representation
$(\frac{1}{2},0) \oplus (0,\frac{1}{2}) $ Representation
$(\frac{1}{2},\frac{1}{2})$ Representation
- infinite dimensional Representation?
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