Two geometric character formulas for reductive Lie groups

Abstract

In this paper we prove two formulas for the characters of representations of reductive groups. Both express the character of a representation π \pi in terms of the same geometric data attached to π \pi . When specialized to the case of a compact Lie group, one of them reduces to Kirillov’s character formula in the compact case, and the other, to an application of the Atiyah-Bott fixed point formula to the Borel-Weil realization of the representation π \pi .