Isometries of Hermitian symmetric spaces
Isometries of Hermitian symmetric spaces
Isometries of Hermitian symmetric spaces
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P = G/K : a Riemannian <strong>symmetric</strong> space <strong>of</strong> compact<br />
type<br />
G = I0(M), K = {g ∈ G | g(o) = o}, o ∈ P<br />
g = k ⊕ p : the canonical decomposition<br />
g = Lie(G), k = Lie(K), p ∼ = ToP<br />
Take ξ(̸= 0) ∈ p with ad(ξ) 3 = −ad(ξ),<br />
then M = Ad G(K)ξ ⊂ p : a <strong>symmetric</strong> R-space<br />
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