I was reading the paper "Division Algebras and Supersymmetry I " By John Baez and John Huerta.
In this paper he constructs representations of Spinors in space time with signature (d+1,1)(d=1,2,4,8) using the Reals, Complex, Quarterniions and Octernions respectively.
In his paper(pdf) on page 6 he says,
- When K = R, S+ ∼ S− is the Majorana spinor representation of Spin(2, 1).
- When K = C, S+ ∼ S− is the Majorana spinor representation of Spin(3, 1).
- When K = H, S+ and S− are the Weyl spinor representations of Spin(5, 1).
- When K = O, S+ and S− are the Majorana–Weyl spinor representations of Spin(9, 1).
Please refer to the paper for further details about their construction.
Is this construction Exhaustive? How does one construct the other possible representations for instance the Weyl representations in (3,1) using division algebras?
Also I request recommendations for further reading material on this subject, which is suitable for a student of physics.