A classification of simple weakly spherical homogeneous spaces. I (Q1920008)

The homogeneous space \(H\setminus G\), defined by a connected linear algebraic group \(G\) (on the field of complex numbers) and a closed subgroup \(H\), is said to be weakly spherical if it admits a Zariski dense \(P\)-orbit, where \(P\) is some parabolic subgroup of \(G\). The authors undertake the task of classifying all such homogeneous spaces for \(G=\text{GL}_n\). This is done here under some additional assumptions, yielding an explicit list of 74 cases.