M Theory Lesson 202

So combining 1-circulants and 2-circulants is interesting in the context of mixing. Let us play with combinations of the Fourier operators for both cases. For example, Recall that these two matrices can be combined to describe an element of $B_{3}$ using a representation linked to the theory of the field with one element. We obtain which is a Bilson-Thompson type braid for particles. Since $U_{2}^{\dagger} U_{1} = U_{1}^{\dagger} U_{2}$, we can rewrite the quadruple product as $U_{1}^{\dagger} ( U_{2} U_{1} U_{2}^{\dagger} )$.