Edmund Karasiewicz (Utah)

The uniqueness of Whittaker models plays an important role in the representation theory of linear reductive groups due to its relation to L-functions. However such uniqueness fails in general for nonlinear covering groups. We investigate this failure of uniqueness through the Gelfand-Graev representation, which is the dual of the Whittaker space.

Using the pro-p Iwahori-Hecke algebra, we describe the Iwahori-fixed vectors in the Gelfand-Graev representation of covering groups as a module over the Iwahori-Hecke algebra, generalizing work of Barbasch-Moy and Chan-Savin for linear groups. As applications, we 1) relate the Gelfand-Graev representation to the metaplectic representation of Sahi-Stokman-Venkateswaran; 2) compute the dimension of the space of Whittaker models for constituents of certain unramified principal series.

This is joint work with Fan Gao and Nadya Gurevich.