Small representations of finite groups

Many properties of a finite group G can be approached using formulas involving sums over its characters.
A serious obstacle in applying these formulas seemed to be lack of knowledge over the low dimensional 
representations of G. In fact, the “small" representations tend to contribute the largest terms to these
sums, so a systematic knowledge of them might lead to proofs of some conjectures which are currently
out of reach.

This talk will discuss a joint project with Roger Howe (Yale), where we introduce a language to define,
and a method for systematically construct, the small representations of finite classical groups. 

I will demonstrate our theory with concrete motivations and numerical data obtained with John Cannon
(MAGMA, Sydney) and Steve Goldstein (Scientific computing, Madison).