Number Theory Seminar
`Small' Representations of Finite Groups
Shamgar Gurevitch: University of Wisconsin
Location: Hill 525
Date & time: Tuesday, 21 February 2017 at 2:00PM - 2:11PM
Suppose you have a finite group G and you want to study certain related structures (e.g., random walks, Cayley graphs, word maps, etc.). In some cases, this might be done using sums over the characters of G. It seems that, in some cases, an obstacle in applying these formulas is lack of control over the low-dimensional representations of G. In fact, numerics shows that the â€œsmall representations tend to contribute the largest terms to these sums, so a systematic knowledge of them might assists in the solution of some interesting problems.
This talk discusses a joint project with Roger Howe (Yale). We introduce a language to speak about â€œsizeâ€ù of a representation, and we develop a method for systematically construct (conjecturally all the) ''small'' representations of finite classical groups.
We will illustrate our theory with concrete motivations and numerical data obtained with John Cannon (MAGMA, Sydney) and Steve Goldstein (Scientific computing, Madison).