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Paper IPM / P / 8399  


Abstract:  
Using the partition of the number p−1 into p−1 real parts which
are not equal with each other necessarily, we develop the unitary
parasupersymmetry algebra of arbitrary order p so that the
wellknown RubakovSpiridonovKhare parasupersymmetry becomes a
special case of the developed one. It is shown that the developed
algebra is realized by simple harmonic oscillator and Landau
problem on a at surface with the symmetries of h_{3} and h_{4}
HeisenbergLie algebras. For this new parasupersymmetry, the
wellknown unitary condition is violated, however, unitarity of
the corresponding algebra is struc turally conserved. Moreover,
the components of the bosonic Hamiltonian operator are derived as
functions from the mean value of the partition numbers with their
label weight function.
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