Structure of Root Data and Smooth Regular Embeddings
One of the key tools when dealing with finite reductive groups is the notion of a regular embedding. Roughly this is a closed embedding of a connected reductive algebraic group into another such group whose centre is connected. The prototypical example of a regular embedding is the natural embedding of the special linear group into the general linear group.
In this talk we consider the notion of a smooth regular embedding, which is a strengthening of the notion of a regular embedding. Here we require that the centre not only be connected but also smooth, which one can take to mean that the centre is connected over a field of characteristic 0. The previously mentioned example is an example of a smooth regular embedding.