RIGIDITY AND AUTOMORPHISM-GROUPS OF SOLVABLE ARITHMETIC GROUPS

A solvable linear algebraic group G which is defined over Q is called reduced if the kernel of the adjoint action of G on the unipotent radi cal R-u(G) is contained in R-u(G). We prove a rigidity theorem for ari thmetic subgroups Gamma of reduced solvable linear algebraic groups. A s an application we give a detailed description of the automorphism gr oup of such groups Gamma. Using an appropriate embedding result we the n show that the automorphism groups of a wide class of arithmetic solv able groups are again arithmetic groups. (C) Academie des Sciences/Els evier, Paris.