The “Spinrps. pdf” file below contains the derivations for the double covering of the rotations group by the SU(2) group and respective of the restricted Lorentz group by the SL(2,C) group and also for the irreducible representations of these groups. We adopt a slightly different definition of a Lie group representation, which representation we will consider to be locally map dependent and therefore fractional spin representations will be allowed, without introducing projective representations.
This chapter you can also find in the post
Notes on … quantum field theory