Theta liftings for loop GL(n) groups

Speaker: Prof. CHEN Yanze (University of Alberta)

Venue: Room 101, Building 2, Haina Court, Zijingang Campus

Abstract: An analogue of the Segal-Shale-Weil representation for loop symplectic groups over a local field was constructed by Zhu 15 years ago. For a reductive dual pair in a symplectic group over a global field, one can thus consider the analogue of the global theta lifting of an automorphic form in the context of loop groups. We computed the theta liftings of a "cusp form" on the loop GL(n) group induced from a "classical" cusp form for the loop group dual pair (GL(n),GL(n)), and explained the result an Eisenstein series. In this computation, an interesting model of the local loop Weil representation is introduced, which is essentially due to Kapranov. This is a joint work with Yongchang Zhu.

Contact person: Prof. LIU Dongwen (maliu@zju.edu.cn）