4/13/2005

Michael Larsen
Indiana University

The Inverse Problem in Invariant Theory

The direct problem in invariant theory is to describe the category of representations of a given group. Its inverse is to extract information about a group from information about its representations. The prototypical result in this direction is Tannaka duality. The ultimate goal is to recognize compact Lie groups which appear in nature, where in practice one typically does not know the category of representations up to isomorphism.