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.
Categories: math.NT