Essential Dimension of Algebraic Groups and Integral Representations of Weyl Groups

Abstract

Upper bounds on the essential dimension of algebraic groups can be found by examining related questions about the integral representation theory of lattices for their Weyl groups. We examine these questions in detail for all simple affine algebraic groups, expanding on work of Lorenz and Reichstein for PGLn. This results in upper bounds on the essential dimensions of these simple affine algebraic groups which match or improve on the previously known upper bounds.