2014/12/30 by Werner Hoffmann, Hoffmann, Werner
Mathematics · #11F72 (Primary) #11M41 (Secondary) #11S90 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:11F72 #msc:11M41 #msc:11S90
paper · pdf · doi:10.48550/arxiv.1412.8673
Submitted to the proceedings of the Simons Symposium "Families of Automorphic Forms and the Trace Formula", January 26 - February 1, 2014 in Rio Grande, Puerto Rico
arxiv created 2014/12/30 · arxiv updated 2014/12/31
We describe an approach to express the geometric side of the Arthur-Selberg trace formula in terms of zeta integrals attached to prehomogeneous vector spaces. This will provide explicit formulas for weighted orbital integrals and for the coefficients by which they are multiplied in the trace formula. We implement this programme for the principal unipotent conjugacy class. The method relies on certain convergence results and uses the notions of induced conjugacy classes and canonical parabolic subgroups. So far, it works for certain types of conjugacy classes, which covers all classes appearing in classical groups of absolute rank up to two.