Is there some good reference for the classification of finite-dimensional ${\mathbb R}$-linear (as opposed to ${\mathbb C}$-linear) representations of $\mathfrak{sl}\_2{\mathbb C}$?


Equivalently, what is a good reference (for mathematicians) for the representation theory of the Lorentz group?



R-linear representations of sl(2,C)
The real-linear representations are sums of irreducibles, and the irreducibles are parametrized by pairs of nonnegative integers: see Knapp's §2.3 [here](http://books.google.com/books?id=QCcW1h835pwC&pg=PA31).


Explicitly the irreducible parametrized by $(m,n)$ acts on the polynomials $f$ in $(z\_1,z\_2,\bar z\_1,\bar z\_2)$ that are homogeneous of degree $m$ in $(z\_1,z\_2)$ and of degree $n$ in $(\bar z\_1,\bar z\_2)$, by
$$
\biggl(\begin{pmatrix}a&b\\c&d\end{pmatrix}f\biggr)
\begin{pmatrix}z\_1\\z\_2\end{pmatrix}=
f\biggl(\begin{pmatrix}a&b\\c&d\end{pmatrix}^{-1}\begin{pmatrix}z\_1\\z\_2\end{pmatrix}\biggr).
$$


