Cyclic cohomology and generalized formal degrees for Affine Hecke algebras

In this talk I will introduce affine Hecke algebras and discuss some of their representation theory, in particular their Fourier transform. We will consider discrete series representations and how their formal degrees can help us understand them. There is no quantity like the formal degree available to help us similarly study limits of discrete series representations. I will sketch how this difficulty might be overcome by using cyclic cohomology and its pairing with K-theory to introduce generalized formal degrees.