  We investigate the dynamical symmetry superalgebras of the one-dimensional
Matrix Superconformal Quantum Mechanics with inverse-square potential. They act
as spectrum-generating superalgebras for the systems with the addition of the
de Alfaro-Fubini-Furlan oscillator term. The undeformed quantum oscillators are
expressed by $2^n\times 2^n$ supermatrices; their corresponding
spectrum-generating superalgebras are given by the $osp(2n|2)$ series. For
$n=1$ the addition of a inverse-square potential does not break the $osp(2|2)$
spectrum-generating superalgebra. For $n=2$ two cases of inverse-square
potential deformations arise. The first one produces Klein deformed quantum
oscillators; the corresponding spectrum-generating superalgebras are given by
the $D(2,1;\alpha)$ class, with $\alpha$ determining the inverse-square
potential coupling constants. The second $n=2$ case corresponds to deformed
quantum oscillators of non-Klein type. In this case the $osp(4|2)$
spectrum-generating superalgebra of the undeformed theory is broken to
$osp(2|2)$. The choice of the Hilbert spaces corresponding to the admissible
range of the inverse-square potential coupling constants and the possible
direct sum of lowest weight representations of the spectrum-generating
superalgebras is presented.
