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The two dimensional Hamiltonian with generalized shape invariance
symmetry over S2, has been obtained via Fourier transformation
over the three coordinates of the SU(3) Casimir operator defined
on $SU(3)/SU(2)$ symmetric space. It is shown that the generalized
shape invariance is equivalent to SU(3) symmetry and that there is
one to one correspondence between the representations of the
generalized shape invariance and SU(3) Verma modules. Also the two
dimensional Hamiltonian in R2 space which posseses ordinary shape
invariance symmetry with respect to two parameters, has been
obtained via In?n?Wigner contraction over SU(3) manifold.
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