Spin representations and binary numbers
We consider a construction of the fundamental spin representations of the simple Lie algebras in terms of binary arithmetic of fixed width integers. This gives the spin matrices as a Lie subalgebra of a -graded associative algebra (rather than the usual -filtered Clifford algebra). Our description gives a quick way to write down the spin matrices, and gives a way to encode some extra structure, such as the real structure which is invariant under the compact real form, for some . Additionally...