  We study the solutions to the Dirac equation for the massive spinor field in
the universal covering space of two-dimensional anti-de Sitter space. For
certain values of the mass parameter, we impose a suitable set of boundary
conditions which make the spatial component of the Dirac operator self-adjoint.
Then, we use the transformation properties of the spinor field under the
isometry group of the theory, namely, the universal covering group of
$\mathrm{SL}(2,\mathbb{R})$, in order to determine which self-adjoint boundary
conditions are invariant under this group. We identify the corresponding
solution spaces with unitary irreducible representations of this group using
the classification given by Pukanzki, and determine which of these correspond
to invariant positive- and negative-frequency subspaces and, hence, in a vacuum
state invariant under the isometry group. Finally, we examine the cases where
the self-adjoint boundary condition leads to an invariant theory with
non-invariant vacuum state and determine the unitary representation to which
the vacuum state belongs.
