special relativity - Vector spaces for the irreducible representations of the Lorentz Group

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?