Student Combinatorics and Algebra Seminar


Abstract 

In this talk, we discuss the classification of reductive groups over R. When working over C, the classification of reductive groups reduces to checking root data, a combinatorial problem. Over R, the classification is more subtle. Two nonisomorphic real reductive groups may share root datae.g. SL_n(R) and SU(n). The solution to this phenomenon is to consider socalled relative root data, essentially complex root data together with a Galois action. We discuss the interaction of conjugation with root systems and how it manifests in the classification, structure theory, and geometry of real reductive groups. 