Research project: K-theory and cyclic homology of affine Weyl groups
Affine and extended affine Weyl groups play a significant role in the classification of real and complex semi-simple Lie groups encoding the symmetries of their root and coroot lattices. Langlands duality is a duality between Lie groups which arises by interchanging roots and coroots, and this duality induces a duality at the level of the affine and extended affine Weyl groups. We showed that this duality is also related to the Baum-Connes isomorphism in K-theory, and in this project we are carrying out the explicit calculations necessary to understand this isomorphism, providing a whole new family of examples to illuminate the mysterious assembly map.