La imagen del homomorfismo de Lepowsky para todo grupo de Lie semisimple de rango split uno

O.A. BREGA, L.CAGLIERO Y J. TIRAO

Universidad Nacional del Sur, Bahía Blanca

Congreso; LVI Reunión Anual de la Unión Matemática Argentina; 2006

Unión Matemática Argentina

Let G_o be a  rank one semisimple Lie group and let K_o denote a maximal compact subgroup of G_o. Let U(g) be the complex universal enveloping algebra of G_o and let U(g)K denote the centralizer of K_o in U(g). Also let P be the projection map from U(g) onto the tensor product of U(k) and U(a), corresponding to the direct sum U(g)=(U(k) tensor U(a))+U(g)n associated to an Iwasawa decomposition of G_o adapted to K_o. In this paper we give a characterization of the image of U(g)^K under the injective antihomorphism P into U(k) tensor U(a).