Explain to me in the simplest terms triality?
The gamma matrices are 16-dimensional, but the 16-dimensional representation space decompose into two 8-dimensional spinor representations. Yes I mean inverse by ^(-1). I must admit I don't know the mathematical details of triality (yet), other than the fact that it's a symmetry of the roots system of Spin(8). I'm sure other people can help, but I suppose you won't understand it without learning about the mathematics of roots systems in Lie theory.