Geometry Seminar

Date: April 23, 2018

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Shamgar Gurevich, University of Wisconsin

Title: A look on Representations of SL(2,q) through the Lens of Size

Abstract: How to study a nice function f of the real line? A physically motivated technique (called Harmonic analysis/Fourier theory) is to expand f in the basis of exponentials (also called frequencies) and study the meaningful terms in the expansion. Now, suppose f lives on a finite non-commutative group G, and is invariant under conjugation. There is a well-known analog of Fourier analysis, using the irreducible characters of G. This can be applied to many functions f that express interesting properties of G. To study f we want to know: Question: Which characters contributes most for the sum? I will describe for you the G=SL(2,Fq) case of the theory we are developing with Roger Howe (Yale/Texas A&M), which attempts to answer the above question. Remark: The irreducible representations of SL(2,Fq) are “well known” for a very long time and are a prototype example in many introductory course on the subject. So, it is nice that we can say something new about them. In particular, it turns out that the representations that people classify as “anomalies” in the old theory are the building blocks of our new theory.