Abstract: We will start from representation theory of finite groups. I will define representation, and explain some basic notions such as irreducible representation, regular representation, character, restriction and induction, Mackey theory. Then I will intuitively explain how some of those notions generalize to unitary representations of the infinite (but algebraic and reductive) group GL(n,R), consisting of invertible n by n matrices with real entries. To every irreducible unitary representation of GL(n,R) we will attach several partitions of the number n that measure the size of this representation in several ways. Our recent result, joint with Siddhartha Sahi, says that all those partitions coincide. If time permits, we will also formulate a result on non-unitary admissible representations.

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at Schreiber building 006