Hermitian Symmetric Spaces
A symmetric space with a compatible complex structure is called Hermitian. The compact simply connected irreducible Hermitian symmetric spaces fall into 4 infinite families with 2 exceptional ones left over, and each has a non-compact dual. In addition the complex plane is also a Hermitian symmetric space; this gives the complete list of irreducible Hermitian symmetric spaces.
The four families are the types A III, B I and D I for p=2, D III, and C I, and the two exceptional ones are types E III and E VII of complex dimensions 16 and 27.
Read more about this topic: List Of Simple Lie Groups
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