School of Mathematical Sciences

The Conductor and the Newform for Representations of GL_n(R) and GL_n(C) menu

The Conductor and the Newform for Representations of GL_n(R) and GL_n(C)

Speaker: 
Peter Humphries (UCL)
Date/Time: 
Mon, 23/10/2017 - 16:30
Room: 
Queens W316
Seminar series: 

There is a well-known theory of decomposing spaces of automorphic forms into subspaces spanned by newforms and oldforms, and associated to a newform is its conductor. This theory can be reinterpreted as a local statement, and generalised to GL_n, as distinguishing certain vectors in a generic irreducible admissible representation of GL_n(F), where F is a nonarchimedean local field, and associating to this representation a conductor (or rather, a conductor exponent). Such a local theory was previously not well understood for archimedean fields. In this talk, I will introduce this theory in this hitherto unexplored setting.