Unified theory for external and internal attributes and symmetries of fundamental fermions Ikuo S Sogami -Hierarchy of the parasupersymmetric Hamiltonians in quantum mechanics V P Spiridonov -This content was downloaded from IP address 207.241.229.225 on 11/11 Abstract. We construct a para SUSY Virasoro algebra by generalizing the ordinary fermion in SUSY Virasoro algebra (Ramond or Neveu-Schwarz algebra) to the parafermion. First, we obtain a polynomial relation (PR) between different-mode

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... fermion fi's by generalizing the corresponding single-mode PR to such that is invariant under the unitary transformation of fi (Green's condition). Differently from a usual context, where the Green's condition is imposed only on the defining relation of fi (degree three with respect to fi and f † i ), we impose it on any degree of PR. For the case of order-two parafermion (the simplest case of para SUSY), we calculate a PR between the parasupercharge G0, the bosonic hamiltonian L B 0 and parafermionic one L F 0 , although it is difficult to obtain a PR between G0 and the total hamiltonian L0 (= L B 0 + L F 0 ). Finally, we construct a para SUSY Virasoro algebra by generalizing L0 to the Ln's such that form a Virasoro algebra.