Joint IAS/Princeton University Number Theory Seminar

This talk is based on some results for real groups used in Arthur's classification of global packets for classical groups. The setting is twisted endoscopy for a connected reductive algebraic group over the reals. There is a geometric transfer which generates useful test functions on the real points of an endoscopic group. I will discuss some of this, mainly to look at structure of the weights, or transfer factors, attached to pairs of conjugacy classes. Then I will introduce a parallel definition of factors based on representations instead of conjugacy classes. As in the geometric case the factors simplify when a Whittaker normalization is available. Results so far indicate that these spectral factors provide exactly the refined form of dual transfer needed globally.