  Recently, Gekeler proved that the group of invertible analytic functions
modulo constant functions on Drinfeld's upper half space is isomorphic to the
dual of an integral generalized Steinberg representation. In this note we show
that the group of invertible functions is the dual of a universal extension of
that Steinberg representation. As an application, we show that lifting
obstructions of rigid analytic theta cocycles of Hilbert modular forms in the
sense of Darmon--Vonk can be computed in terms of $\mathcal{L}$-invariants of
the associated Galois representation. The same argument applies to theta
cocycles for definite unitary groups.
