  A shape invariant nonseparable and nondiagonalizable two-dimensional model
with quadratic complex interaction, first studied by Cannata, Ioffe, and
Nishnianidze, is re-examined with the purpose of exhibiting its hidden
algebraic structure. The two operators $A^+$ and $A^-$, coming from the shape
invariant supersymmetrical approach, where $A^+$ acts as a raising operator
while $A^-$ annihilates all wavefunctions, are completed by introducing a novel
pair of operators $B^+$ and $B^-$, where $B^-$ acts as the missing lowering
operator. These four operators then serve as building blocks for constructing
${\mathfrak{gl}}(2)$ generators, acting within the set of associated functions
belonging to the Jordan block corresponding to a given energy eigenvalue. This
analysis is extended to the set of Jordan blocks by constructing two pairs of
bosonic operators, finally yielding an ${\mathfrak{sp}}(4)$ algebra, as well as
an ${\mathfrak{osp}}(1/4)$ superalgebra. Hence, the hidden algebraic structure
of the model is very similar to that known for the two-dimensional real
harmonic oscillator.
