On the varieties of parabolic subgroups, their generalizations and combinatorial applications (Q1270644)

Let \((G:P)\) be the varieties of Chevalley groups \(G\) by their maximal parabolic subgroups \(P\). The author discusses interpretations of varieties \((G:P)\) and small Schubert cells in terms of linear algebra, generalizations of varieties to the case of Kac-Moody algebras and superalgebras, and applications to extremal graph theory.