“School of Physics”
Back to Papers HomeBack to Papers of School of Physics
Paper IPM / P / 6738  


Abstract:  
By introducing a new parameter as a second associated index for
special functions, we construct the threedimensional differential
generators of gl(2,c) Lie algebra together with the
corresponding contracted form h_{4}. NonCasimir quadratic as
well as the Casimir of gl(2,c) (and h_{4}) generators
can be considered as quantum solvable models on group manifold
SL(2,c). Then, by appropriate parametrization of group
manifold SL(2,c) and eliminating one of the coordinates,
we obtain quantum solvable Hamiltonians on homogeneous manifold
SL(2,c)÷GL(1,c) with the metric described by
master function. We show that twodimensional Hamiltonian on
SL(2,c)÷GL(1,c) derived from the reduction of
Casimir operator so(4,c) Lie algebra as a
threedimensional Hamiltonian on group manifold SL(2,c),
possesses the degeneracy SL(2,c) group and, also, the
shape invariance property, where both have parasupersymmetry
representations of arbitrary order.
Download TeX format 

back to top 