Let G be a reductive p-adic group. Let W be a weyl group. if x,y in W I want to know in which case we have x y x^-1 = y ?

in case if y(θ)=θ where θ is a subset of simple roots, and x is the longest element in W_θ, the subgroup of W generated by s_α (simple reflection of α), where α is in θ.

thanks.