The quotient of a Lie group by the Levi factor of a parabolic subgroup - MathOverflow

The quotient of a Lie group by the Levi factor of a parabolic subgroup

2011-02-04T11:13:26Z

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.

Answer by robot for The quotient of a Lie group by the Levi factor of a parabolic subgroup

2011-02-06T21:06:33Z

Exhausting account on homogeneous spaces of the form $G/P$ with $G$ semisimple and $P$ parabolic is given in this book. The relationship between $P$ and $L$ is also explained there in detail so presumably one may take these results as a starting point.