Notes on Doubly Extended Groups

(3) G = 〈G, δ〉, G = 〈G, ǫ〉. We think of τ as given an inner class of real forms of G; G = 〈G, δ〉 is the the usual extended group. By a strong real form for G we mean with respect to G, i.e. in the inner class of τ . The involution μ is secondary. An important special case is μ = τ , which governs Hermitian representations of strong real forms G (in the inner class of τ). Often on the dual side μ 6= τ .