I have 3 operators $A$, $B$ and $C$ that can be combined to yield the SU(2) commutation relations:
\begin{align} \frac12(C+C^\dagger)\approx X\\ \frac{1}{2i}(C-C^\dagger)\approx Y\\ \frac12(A-B)\approx Z \end{align} with \begin{align} [X,Y]=2iZ\\ [Y,Z]=2iX\\ [Z,X]=2iY \end{align}
I'm trying to find a computationally efficient way to compute the matrix elements of $$\exp(aA + bB +cC +dC^\dagger)$$ when $A$, $B$ and $C$ are given as infinite-dimensional matrices.
How can I exploit the correspondence with the algebra of SU(2) to compute the exponential?