I am reading Hitchin’s “self-duality equations on a Riemann Surface”, in which Sec.2 there is an expression $U(2)/Z(U(2))\cong SO(3)$, what is the homomorphism $U(2)$ to $SO(3)$?
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1The center of a group $G$ is usually denoted by $Z(G)$. For matrix groups, diagonal matrices are in the center. In this case, we can use such matrices to get a "normed" version with determinant one. Furthermore, note that $\pm 1$ are such matrices. Then a good place to look at is... https://math.stackexchange.com/questions/185472/how-to-show-su2-mathbbz-2-cong-so3 – dan_fulea Jun 16 '21 at 07:36
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Google "SU(2) SO(3)" – anon Jun 16 '21 at 08:16