Question

What is the physical implication of a homomorphism between SU(2) and SO(3)?

Answer 1

You should specify a theory related to SU(2)SU(2) or SO(3)SO(3) you are interested in. Also, there is no genereral homomorphism between SU(n)SU(n) and SO(3)SO(3) or SU(n)SU(n) and SO(n)SO(n). A homomorphism (with implications to physics) would be one between Spin(n)Spin(n) and SO(n)SO(n).

Answer 2

A theory related to SU(2) or SO(3) you are interested in.

Also, there is no general homomorphism between SU(n) and SO(3) or SU(n) and SO(n).

A homomorphism (with implications to physics) would be one between Spin(n) and SO(n)