Representation theory Seminar

Abstract
Representation theory is a vast subject, and in three talks, I can just give some glimpses into the subject.
Starting from first principles ( there are no real pre-requisites for this mini-course) I will treat three examples in some detail:

-- the quaternionic group $Q_8$ and its representations

-- the group $SL_2(F)$ over a finite field $F$, principal series, cuspidal representations, parameters

-- the group $SL_2(\mathbb{R})$, principal series, analogy with $SL_2(F)$, cusp forms and discrete series