"Small" representations of finite classical groups

Seminar
Speaker
Prof. Shamgar Gurevich (University of Wisconsin and Yale University)
Date
01/02/2017 - 11:30 - 10:30Add to Calendar 2017-02-01 10:30:00 2017-02-01 11:30:00 "Small" representations of finite classical groups 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 many cases, this might be done using sums over the characters of G. A serious obstacle in applying these formulas is lack of knowledge on the low dimensional representations of G. In fact, numerics shows that the “small" representations tend to contribute the largest terms to these sums, so a systematic knowledge of them might assist in the solution of important problems.  In this talk I will discuss a joint project (see arXiv:1609.01276) with Roger Howe (Yale). We introduce a language to speak about “size” of a representation, and we develop a method for systematically construct (conjecturally all the) “small" representations of finite classical groups. I will illustrate our theory with concrete motivations and numerical data obtained with John Cannon (MAGMA, Sydney) and Steve Goldstein (Scientific computing, Madison).  Third floor seminar room אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Third floor seminar room
Abstract

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 many cases, this might be done using sums over the characters of G. A serious obstacle in applying these formulas is lack of knowledge on the low dimensional representations of G. In fact, numerics shows that the “small" representations tend to contribute the largest terms to these sums, so a systematic knowledge of them might assist in the solution of important problems. 

In this talk I will discuss a joint project (see arXiv:1609.01276) with Roger Howe (Yale). We introduce a language to speak about “size” of a representation, and we develop a method for systematically construct (conjecturally all the) “small" representations of finite classical groups.

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

Last Updated Date : 21/12/2016