Isometries of Hermitian symmetric spaces

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I(P ) is generated by I(P1) × · · · × I(Pr) and by all permutations of isometric irreducible factors of P . Since permutations of isometric irreducible factors of P extend to permutations of the corresponding simple factors of g (possibly up to sign on some factors), we may assume that P is irreducible. 18
Let f ∈ I(P ). Let m be the midpoint of a geodesic arc between o to f(o), then sm ◦ f(o) = o. Since P is an extrinsically symmetric submanifold of g and sm has the extension ρm, we may assume that f(o) = o. 19
Page 1 and 2: Isometries of Hermitian symmetric s
Page 3 and 4: 1. Introduction A Riemannian symmet
Page 5 and 6: M : a Riemannian manifold τ : an i
Page 7 and 8: 2. Extrinsically symmetric spaces M
Page 9 and 10: P = G/K : a Riemannian symmetric sp
Page 11 and 12: I(M) : the group of isometries of M
Page 13 and 14: 3. Isometries of Hermitian symmetri
Page 15 and 16: Consider the map ι : P → g, p
Page 17: Proof: P = P1 × · · · × Pr : a
Page 21 and 22: Lemma (I f)∗(Jo) ∈ {±Jo}. Proo
Page 23 and 24: Remark It is a known fact that ever
Page 25 and 26: 4. Another result Theorem 2 (Loos 1
Page 27 and 28: Proposition 3 Let M be a compact Ri
Page 29: Further, a meridian M − of X is e

Isometries of Hermitian symmetric spaces

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