Symmetric Spaces: Compact spaces and classification

a₁ acts Assume basis belongs called cell Chapter Choose classification Clearly compact complex component computation conjugate considered containing Conversely Corollary corresponding covering decomposable decomposition defined definite denote determined dimension domain dual Dynkin diagram elements exists extended fact finite fixed point follows given gives Hence Hermitian hyperplane induces inner invariant involutive automorphism isomorphic Jordan algebra lattice leaves Lemma Lie algebra Lie group linear form maximal torus metric multiplicity normal Note orthogonal outer positive possibilities Proof Proposition Proposition 1.4 prove rank reduced reflection relative representation resp root system semisimple shows simply connected structure subgroup subset symmetric space Table Theorem Theorem 3.4 tion trace transformation transitive triple uniquely unit vector Weyl chamber Weyl group X₁ α α