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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.

John
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  • Your should specify if you are interested in finite-dimensional or infinite-dimensional representations. 2. The group $SU(1,1)$ is isomorphic to $SL(2,R)$. The (finite-dimensional) real representation theory of the latter is the same as the complex representation theory of $SL(2,C)$, which is discussed in great detail in any textbook on representation theory. As for $SO(1,1)$, it is isomorphic to the product $Z_2\times R$. Thus, its representation theory is essentially the same as of $R$.
    • – Moishe Kohan Nov 10 '19 at 13:44