Hecke operators and generalized group characters
by Nora Ganter
Abstract: Elliptic cohomology is a field at the intersection of algebraic topology, number theory, and algebraic geometry. Its definition is technical and highly homotopy theoretic. While a conjectured geometric definition is still an open question, elliptic cohomology exhibits striking formal similarities to string theory, and it is strongly expected that a geometric interpretation will come from there. More recently, it has become apparent that 2-categories will have an important role to play.
To illustrate the interaction between the various fields, I will speak
about my work on generalized group characters.
I will start with a very informal introduction to elliptic cohomology and Hopkins-Kuhn-Ravenel (HKR) character theory. Since these HKR characters carry a strong resemblance to characters of group representations, it seems natural to look for the representation theory that yields them as its characters. I will describe a joint project with Kapranov on characters of categorical representations that aims to provide an answer to this question.
I will then outline connections to generalized Moonshine and orbifold string theory and explain how the Hecke operators act in the different scenarios.
For More Information: Professor Peter Taylor P.Taylor@ms.unimelb.edu.au