Event № 283
For a finite group G one can consider important structures such as: Expander Graphs, Random Walks, Word Maps, etc. Many properties of these structures can be approached using “Fourier type” sums over the characters of representations of G.
A serious obstacle in applying these Fourier sums, seems to be a lack of control over the dimensions of representations of G.
In my talk, for the sake of clarity, I will discuss only the case of the finite special linear group G=SL(2,F_q). I will show how one can solve several interesting problems by ordering and constructing the representations of G according to their “size”.
This talk is an example from a joint project with Roger Howe (Yale), where we introduce a language to define the “size" of representations, and develop a method to construct representations of finite classical groups according to their “size".
The lecture is accessible to advanced undergraduate students.