Iwasawa Decomposition for Lie Superalgebras

Let g be a basic simple Lie superalgebra over an algebraically closed field of characteristic zero, and θ an involution of g preserving a nondegenerate invariant form. We prove that at least one of θ or δ 0 θ admits an Iwasawa decomposition, where δ is the canonical grading automorphism δ(x) = (-1)xx. The proof uses the notion of generalized root systems as developed by Serganova, and follows from a more general result on centralizers of certain tori coming from semisimple automorphisms of the Lie superalgebra g.