Seminar: Mapping class groups and difference operators
- Date: 12/7/2017 at 10:00 AM – 11:00 AM
- Location: Å73121
- Lecturer: Shamil Shakirov (Harvard)
- Contact person: Fabrizio Nieri
We review the representation of SL(2,Z) -- the mapping class group of the torus -- by automorphisms of a simple algebra of difference operators. The algebra, known as spherical double affine Hecke algebra (DAHA) plays an important role in many developments in modern representation theory and mathematical physics. We will define a new algebra which is a direct analogue of spherical DAHA for a genus two surface, and sketch the proof of the corresponding mapping class group action. Time permitting, we will explain the connection to the Reshetikhin-Turaev construction, and possible generalizations to higher genus.