English

Remarks on the Fundamental Lemma for stable twisted Endoscopy of Classical Groups

Representation Theory 2013-02-04 v1

Abstract

The twisted fundamental lemmas for three series of stable twisted endoscopy (Sp_{2n} to PGL_{2n+1}, GSpin_{2n+1} to GL_{2n}\times GL_1, Sp_{2n} to SO_{2n+2}) will be reduced to a fundamental-lemma-like statement for ordinary (i.e. untwisted) stable orbital integrals on the groups \SO2n+1\SO_{2n+1} of type BnB_n resp. \SP2n\SP_{2n} of type CnC_n. This manusript, written around 2001, anticipates similar results of Waldspurger (2008), and may be used to reduce the twisted fundamental lemma to the work of Ngo. The original aim was to reduce the fundumantal lemma for the lift from Sp_4 to PGL_5 to the twisted fundamental lemma for the lift from GSp_4=GSpin_5 to Gl_4 \times GL_1.

Keywords

Cite

@article{arxiv.1302.0034,
  title  = {Remarks on the Fundamental Lemma for stable twisted Endoscopy of Classical Groups},
  author = {Joachim Ballmann and Rainer Weissauer and Uwe Weselmann},
  journal= {arXiv preprint arXiv:1302.0034},
  year   = {2013}
}