Editing Simple Lie group (section)

===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&nbsp;III, B&nbsp;I and D&nbsp;I for {{nowrap|1=''p'' = 2}}, D&nbsp;III, and C&nbsp;I, and the two exceptional ones are types E&nbsp;III and E&nbsp;VII of complex dimensions 16 and 27.