Table 1 Comparison between SU(2) and SU(3) pictures.

From: 3 parafermionic chain emerging from Yang-Baxter equation

Type of spin sites

SU(2)

SU(3)

Ladder operators

After J-W transform.

Quasiparticle

(Majorana fermions)

Commutation relation

γiγj = −γjγi;

Braid operator

.

Cyclic operation