2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76506In this paper we prove two formulas for the characters of representations of reductive groups. Both express the character of a representation in terms of the same geometric data attached to it. 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.Representation TheoryAlgebraic Geometrytext