Transfer Factors for Lie

Let G be a quasi-split connected reductive group over a local eld of characteristic 0, and x a regular nilpotent element in the Lie algebra g of G. A theorem of Kostant then provides a canonical conjugacy class within each stable conjugacy class of regular semisimple elements in g. Normalized transfer factors take the value 1 on these canonical conjugacy classes. 1. Introduction Let k 0 be a local eld of characteristic 0, let k be an algebraic closure of k 0 , and let ? denote the Galois group of k over k 0. Let G be a connected reductive group over k 0 , with Lie algebra g. We write g(k 0) for the set of k 0-rational points on g.