Graded parafermions: standard and quasiparticle bases Original Research Article

Two bases of states are presented for modules of the graded parafermionic conformal field theory associated to the coset osp(1,2)k/û(1). The first one is formulated in terms of the two fundamental (i.e., lowest-dimensional) parafermionic modes. In that basis, one can identify the completely reducible representations, i.e., those whose modules contain an infinite number of singular vectors; the explicit form of these vectors is also given. The second basis is a quasiparticle basis, determined in terms of a modified version of the Z2k exclusion principle. A novel feature of this model is that none of its bases are fully ordered and this reflects a hidden structural Z3 exclusion principle.