La imagen del homomorfismo de Lepowsky para todo grupo de Lie de rango 1

O. BREGA, L. CAGLIERO Y J. TIRAO

Universidad Nacional del Sur, Bahía Blanca

Congreso; LVI Reunión de comunicaciones científicas; 2006

Unión Matemática Argentina

Let G_o be a  rank one semisimple Lie group and let K_o denote amaximal compact subgroup of G_o. Let U(g) be the complexuniversal enveloping algebra of G_o and let U(g)^K denote thecentralizer of K_o in U(g). Also letP be the projection map from U(g) onto the tensor product of U(k) and U(a), corresponding to the direct sumU(g)=(U(k) tensor U(a))+U(g)n associated to an Iwasawa decomposition of G_o adapted to K_o. In this paperwe give a characterization of the image of U(g)^K under the injectiveantihomorphism P into U(k) tensor U(a).