Equivariant Embeddings of Reductive Groups

Abstract

The main result of this chapter asserts that any equivariant embedding of a connected reductive group G admits a canonical splitting which compatibly splits all the G × G-orbit closures. Here, by an equivariant embedding of G we mean a normal G × G-variety containing an open orbit isomorphic to G itself, where G × G acts on G by left and right multiplications.