  Continuum models for time-reversal (TR) invariant topological insulators
(TIs) in $d \geq 3$ dimensions are provided by harmonic oscillators coupled to
certain $SO(d)$ gauge fields. These models are equivalent to the presence of
spin-orbit (SO) interaction in the oscillator Hamiltonians at a critical
coupling strength (equivalent to the harmonic oscillator frequency) and leads
to flat Landau Level (LL) spectra and therefore to infinite degeneracy of
either the positive or the negative helicity states depending on the sign of
the SO coupling. Generalizing the results of Haaker et al. to $d \geq 4$, we
construct vector operators commuting with these Hamiltonians and show that
$SO(d,2)$ emerges as the non-compact extended dynamical symmetry. Focusing on
the model in four dimensions, we demonstrate that the infinite degeneracy of
the flat spectra can be fully explained in terms of the discrete unitary
representations of $SO(4,2)$, i.e. the {\it doubletons}. The degeneracy in the
opposite helicity branch is finite, but can still be explained exploiting the
complex conjugate {\it doubleton} representations. Subsequently, the analysis
is generalized to $d$ dimensions, distinguishing the cases of odd and even $d$.
We also determine the spectrum generating algebra in these models and briefly
comment on the algebraic organization of the LL states w.r.t to an underlying
"deformed" AdS geometry as well as on the organization of the surface states
under open boundary conditions in view of our results.
