  In this paper we study the analyticity of the group action of the
automorphism group $G$ of a formal module $\bar{F}$ of height 2 (defined over
$\overline{\mathbb{F}}_q$) on the Lubin-Tate deformation space $X$ of
$\bar{F}$. It is shown that a wide open congruence group of level zero attached
to a non-split torus acts analytically on a particular disc in $X$ on which the
period morphism is not injective. For certain other discs with larger radii
(defined in terms of quasi-canonical liftings) we find wide open rigid analytic
groups which act analytically on these discs.
