How to attach a representation to a pair (x,y) Atlas of Lie Groups Workshop
نویسنده
چکیده
Let (G; ) be given. Here G is an algebraic group and an involution in Out(G) determining an inner class of real forms. Fix a Cartan subgroup and a BorelH B G and a set of root vectors fX g. This determines a unique distinguished involution of G mapping to and xing the pinning (H;B; fX g). Form the extended group G = Go , where = f1; g is the Galois group of C over R, and acts on G by the involution . Write = 1 , so G = G t G . Let (G_; _) be the dual group and the involution dual to , and choose the corresponding objects _; H_, B_, and (G_) . We have also made various identi cations h ' h_, X (H) = X (H_), etc.
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