Gelfand-Graev representation for covering groups and applications.

Nadya Gurevich (Ben-Gurion U, Beer-Sheva)

Apr 15. 2022, 09:30 — 10:15


The multiplicity one theorem for the Whittaker model, being such a useful tool in the representation theory of linear groups, fails for covering groups.

 Gelfand-Graev representation V of a linear or covering group G admits  any irreducible  generic smooth representation as a quotient.

We study the space of Iwahori-fixed vectors of V for the case G is a covering group, and present several applications of the description, among them

1. determination of dimensions of Whittaker spaces of constituents of principal series ( regular and unitary cases)

2.  conceptual construction of Chinta-Gunnells action.

3. recursive relations for the spherical Whittaker function for coverings of SL(2).

This is a joint work with Fan Gao and Edmund Karasiewicz.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Minimal Representations and Theta Correspondence (Workshop)
Wee Teck Gan (U of Singapore)
Marcela Hanzer (U Zagreb)
Alberto Minguez (U of Vienna)
Goran Muic (U Zagreb)
Martin Weissman (UC Santa Cruz)