I am interested in some references on the quotient spaces obtained by quotienting G, a simple Lie group, by L, the group generated by the Levi factor of a parabolic subalgebra.

Presumably the case where L is the maximal torus is understood?

I am mostly interested in the compact case.

`$n$`

-sphere have been studied as homogeneous spaces of special orthogonal groups, etc. The question as written is too broad. What books on Lie groups have you already looked at? – Jim Humphreys Feb 4 '11 at 23:08