Let $\mathfrak{ g}$ be a basic simple Lie superalgebra over an algebraically closed field of characteristic zero, and $\theta$ an involution of $\mathfrak{ g}$ preserving a nondegenerate invariant form. We prove that either $\theta$ or $\delta\circ\theta$ admits an Iwasawa decomposition, where $\delta$ is the canonical grading automorphism $\delta(x)=(-1)^{ \overline{ x}}x$. 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 $\mathfrak{ g}$.
Categories: math.RT