Admissible pairs of Hermitian symmetric spaces in the perspective of the theory of varieties of minimal rational tangents

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We study a pair (S₀,S) of irreducible Hermitian Symmetric Spaces of compact type (cHSS) in this paper, with the first aim being classifying all the admissible pairs (S₀,S)). This notion is a natural generalization of the pairs of sub-diagram type originated by Jaehyun Hong and Ngaiming Mok ([HoM 10]). Based on this classification, we partially solve the rigidity problem for the admissible pairs (S₀,S) which was raised by Mok and Zhang (2014) ([MoZ 14]), culminating in determining a sufficient condition for the pairs being non-rigid and proving that special pairs, which show up in the classification procedure, are algebraic, as a weaker result than being rigid. However, whether special pairs are rigid or not remains unknown and needs further investigation in the framework of VMRT theory.