The group of SL(2,C) is sometimes defined (by physicists) as the group of 2 X 2 complex matrices of determinant = 1. But then we can talk about other representations of SL(2,C). So apparently the set of 2 X 2 complex matrices of determinant = 1 is but one representation of SL(2,C). If so, what then is the more formal definition of SL(2,C) ? And what does another irreducible representation or SL(2,C) look like?