_{-}^{\bot }\right) ^{\left( g_{+},X_{+}^{\bot }\right) } \\  \\  \mathrm{Ad}_{\left( g_{-},X_{-}^{\bot }\right) }^{H}\left( X_{+},Y_{+}^{\bot }\right) =\left( g_{-},X_{-}^{\bot }\right) ^{\left( X_{+},Y_{+}^{\bot }\right) }