### Article

## A criterion of smoothness at infinity for an arithmetic quotient of the future tube

Let Γ be an arithmetic group of affine automorphisms of the n-dimensional future tube *T*. It is proved that the quotient space *T*/Γ is smooth at infinity if and only if the group Γ is generated by reflections and the fundamental polyhedral cone (“Weyl chamber”) of the group *d*Γ in the future cone is a simplicial cone (which is possible only for *n* ≤ 10). As a consequence of this result, a smoothness criterion for the Satake–Baily–Borel compactification of an arithmetic quotient of a symmetric domain of type IV is obtained.