Unipotent centralizers in algebraic groups.
Let \(G\) be a simple algebraic group over an algebraically closed field \(K\) of characteristic \(p>0\) with \(p\) a good prime for \(G\). Let \(u\in G\) be unipotent. Canonical embeddings of \(u\) in Abelian unipotent subgroups are studied to obtain results about \(C_G(u)\) -- in particular, \(Z(C_G(u))\) and the reductive part of \(C_G(u)\). In earlier work of the author, the case where \(u\) has order \(p\) was studied and some very elegant results obtained. It turns out that there is a \(1\)-dimensional torus \(T\) acting without fixed points on the connected component \(A\) of \(Z(C_G(u))\) and that \(A\) decomposes nicely as a \(T\)-module. This enables one to reveal many properties of \(C_G(u)\) in a very natural setting.
scientific article; zbMATH DE number 2117266