These are the simplest non-compact Lie groups. Where can I find a discussion of their representations? In my impression, non-compact Lie groups are quite different from compact ones. I would like to start from some simple ones to gain some feel.
Some books discuss the group $SO(1,3) $ a lot. But evidently, this group has some unique features. So the treatment might not be transplanted onto other $SO(m,n)$ groups.