In 3+1 dim Minkovski spacetime, the classification of particle, that is spin-0, 1/2 , 1..., depends on the representation of the universal covering group of SO(1,3), that is SL(2,C). When we study the particle in d+1 dim Minkovski spacetime, is it still meaningful to say spin0, 1/2, 1...?
My question is:
(1) In d+1 dimensional Minkovski spacetime, in principle we need to study the irreducible representation of Spin(1,d) group to do the classification of particle. Therefore is it still meaningful to say a spin-1/2 partilcle in higher dimensional Minkovski spacetime, becasue spin-1/2 is a representation of Spin(1,3)=SL(2,C).
(2) In general 4 dimensional curved spacetime with no isometry, why is it still meaningful to say particle with spin-0,1/2,1... in curved spacetime?
(3) In particular, in 4-dimensional de-Sitter spacetime with isometry group SO(1,4), why we don't do irreducible representation of SO(1,4) to classify the particles in de-Sitter spacetime? Why do we still say spin-0,1/2,1... in de-Sitter spacetime?
Firstly which books or papers will handle above problems? Secondly I really want to know the irreducible representation of Spin(1,d) group, and where can I find the answers?