Isometries of Hermitian symmetric spaces

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Joint with Jost-Hinrich Eschenburg and Peter Quast Contents 1 Introduction 2 Extrinsically symmetric spaces 3 Isometries of Hermitian symmetric spaces 4 Another result 2
1. Introduction A Riemannian symmetric space M is called a symmetric R-space if M is realized as an orbit of a linear isotropy representation of a Riemannian symmetric space of compact type. Every Hermitian symmetric space M of compact type is a symmetric R-space since M is realized as an adjoint orbit of a compact semisimple Lie group. 3
Page 1: Isometries of Hermitian symmetric s
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 and 18: Proof: P = P1 × · · · × Pr : a
Page 19 and 20: Let f ∈ I(P ). Let m be the midpo
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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