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Paper   IPM / P / 7298
School of Physics
  Title:   Embedding of Dynamical Symmetry Groups U(1,1) and U(2) of A Free Particle on AdS2 and S2 into Parasupersymmetry Algebra
1.  H. Fakhri
2.  J. Sadeghi
  Status:   Published
  Journal: Int. J. Theor. Phys.
  No.:  2
  Vol.:  43
  Year:  2004
  Pages:   457-476
  Supported by:  IPM
Using two different types of the ladder equations realized simultaneously by the associated Gegenbauer functions, we show that all quantum states corresponding to the motion of a free particle on AdS2 and S2 split into infinite direct sums of infinite- and finite-dimensional Hilbert subspaces which represent the Lie algebras u(1,1) and u(2) with the infinite- and finite-fold degeneracies, respectively. In addition, it is shown that the representation bases of Lie algebras with rank one, i.e. gl(2,C), realize the representation of non-unitary parasupersymmetry algebra of arbitrary order. The representation of parasupersymmetry algebra by the Hilbert subspaces which describe the motion of a free particle on AdS2 and S2 with the dynamical symmetry groups U(1,1) and U(2) is concluded as well.

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