School of Mathematical Sciences
Monday, February 21, 2011
Schreiber 006, 12:15
Weizmann Institute of Science
Measuring representations of GL(n,R)
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.
Coffee will be served at 12:00 before the lecture
at Schreiber building 006