The quotient of a Lie group by the Levi factor of a parabolic subgroup - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T05:36:01Z http://mathoverflow.net/feeds/question/54304 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/54304/the-quotient-of-a-lie-group-by-the-levi-factor-of-a-parabolic-subgroup The quotient of a Lie group by the Levi factor of a parabolic subgroup Q.Q.J. 2011-02-04T11:13:26Z 2011-02-06T21:06:33Z <p>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.</p> <p>Presumably the case where L is the maximal torus is understood?</p> <p>I am mostly interested in the compact case.</p> http://mathoverflow.net/questions/54304/the-quotient-of-a-lie-group-by-the-levi-factor-of-a-parabolic-subgroup/54564#54564 Answer by robot for The quotient of a Lie group by the Levi factor of a parabolic subgroup robot 2011-02-06T21:06:33Z 2011-02-06T21:06:33Z <p>Exhausting account on homogeneous spaces of the form \$G/P\$ with \$G\$ semisimple and \$P\$ parabolic is given in this <a href="http://www.ams.org/bookstore-getitem/item=surv-154" rel="nofollow">book</a>. The relationship between \$P\$ and \$L\$ is also explained there in detail so presumably one may take these results as a starting point.</p>