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

O. BREGA, L. CAGLIERO Y J. TIRAO

Enviado

Enviado

Lugar: Enviado; Año: 2006

Let $G_o$ be a classical rank one semisimple Lie group and let $K_o$ denote amaximal compact subgroup of $G_o$. Let $U(lieg)$ be the complexuniversal enveloping algebra of $G_o$ and let $U(lieg)^K$ denote thecentralizer of $K_o$ in $U(lieg)$. Also let$P:U(lieg)longrightarrow U(liek)otimes U(liea)$ be the projection mapcorresponding to the direct sum$U(lieg)=igl(U(liek)otimes U(liea)igr)oplus U(lieg)lien$associated to an Iwasawa decomposition of $G_o$ adapted to $K_o$. In this paperwe give a characterization of the image of $U(lieg)^K$ under the injectiveantihomorphism $P:U(lieg)^Klongrightarrow U(liek)otimes U(liea)$.