Spherical varieties of type A
If \(G\) is a reductive group over an algebraically closed field of characteristic zero, an algebraic normal \(G\)-variety \(X\) is called spherical if it contains an open orbit of a Borel subgroup \(B\) of \(G\). In this article, the author gives a complete classification of spherical varieties for reductive groups of type A. If \(X\) is homogeneous, isomorphic to \(G/H\), then \(H\) is called a spherical subgroup of \(G\). A general spherical variety contains an open orbit isomorphic to a homogeneous spherical variety \(G/H\). Given a specific spherical homogeneous variety \(G/H\), the classification of spherical embeddings having an open orbit isomorphic to \(G/H\) is given by combinatorial data, called colored fans. This part of the classification has already been treated by the author and others. In the present article, the author classifies all homogeneous spherical varieties and their colored fans by means of combinatorial structures given on the root systems of the groups of type A. The main part of the article is devoted to the classification of wonderful varieties of type A.
scientific article; zbMATH DE number 1874458