Abstract
This paper contains a proof a priori (i.e. independent of the classification of Hermitian symmetric spaces) of a theorem on the holomorphic 2-number of a Hermitian symmetric space. If N=G/K is a Hermitian symmetric space, where G is a compact simply connected simple Lie group, T a maximal torus of G and F(T,N) = E1,... , Em is the fixed point set of T in N, then for each pair Ei, Ej there is a two-dimensional sphere Nij ⊂ N such that Ei and Ej are antipodal points of Nij.
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Sánchez, C.U. The Holomorphic 2-Number of a Hermitian Symmetric Space. Geometriae Dedicata 72, 69–81 (1998). https://doi.org/10.1023/A:1005034625117
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DOI: https://doi.org/10.1023/A:1005034625117