The canonical dimension of a semisimple group and the unimodular degree of a root system

Abstract

We produce a short and elementary algorithm to compute an upper bound for the canonical dimension of a spit semisimple linear algebraic group. Using this algorithm we confirm previously known bounds by Karpenko and Devyatov as well as we produce new bounds (e.g. for groups of types F 4 , adjoint E 6 , for some semisimple groups).