Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

I present the fundamentals of representation theory of groups and groupoids. I will define the induced representation, imprimitivity systems and theorems of Mackey and Landsman that allow to move between these concepts. I narrow our discussion to transitive transformation groupoid G ✕ K/G where G is locally compact group and K is its compact subgroup. I am going to show that representation of transformation groupoid is irreducible if and only if inducing representation of subgroup K is irreducible and several other theorems.