Gravitational wavefunctions in JT supergravity

We determine explicit expressions for the continuous two-sided gravitational wavefunctions in supersymmetric versions of JT gravity, focusing mainly on $\mathcal{N}=2$ JT supergravity. Our approach is based on representation theory of the associated supergroup, for which we determine the relevant mixed parabolic matrix elements that implement asymptotic AdS boundary conditions at the quantum level. We match our expressions with those found by solving the energy-eigenvalue equation of arXiv:2207.00408. We discuss gravitational applications by computing several amplitudes of interest, and address how our framework can be generalized further.