Kazdhan-Lusztig algorithm for nonlinear real reductive groups and a conjecture of Kazdhan and Patterson
by
David Renard
Université de Poitiers
Coauthors: P.E. Trapa (Harvard)

We establish a KL-algorithm for computing irreducible genuine characters of nonlinear double covers of linear real reductive groups (for instance the double cover G(n, R) of GL(nR)). We apply this to give a geometric definition of the Kazhdan-Patterson lifting from virtual characters on GL(n, R) to genuine virtual characters on G(n, R) . We give a counterexample to the conjecture stating that the lift of an irreducible character is up to sign an irreducible genuine character or zero.

Date received: March 22, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagt-07.