The image of the Lepowsky homomorphism for the split rank one symplectic group

A. BREGA, L.CAGLIERO AND J. TIRAO

JOURNAL OF ALGEBRA

Elsevier

Año: 2007

0021-8693

Abstract. Let Go be a semisimple Lie group and let Ko denote a maximal compact subgroup of Go. Let U(g) be the complex universal enveloping algebra of Go and let U (g)K denote the centralizer of Ko in U (g). Also let P : U (g) → U (k) ⊗ U (a) be the projection map corresponding to the direct sum U (g) = U (k) ⊗ U (a) ⊕ U(g)n associated to an Iwasawa decomposition of Go adapted to Ko . In this paper we give a characterization of the image of U (g)K under the injective antihomorphism P : U (g)K → U (k) ⊗ U (a), considered by Lepowsky, when Go = Sp(n,1).