Abstract
Let Go be a semisimple Lie group, let Ko be a maximal compact subgroup of Go and let denote the complexification of their Lie algebras. Let G be the adjoint group of and let K be the connected Lie subgroup of G with Lie algebra . If is the universal enveloping algebra of , then will denote the centralizer of K in . Also let be the projection map corresponding to the direct sum associated to an Iwasawa decomposition of Go adapted to Ko. In this paper, we give a characterization of the image of under the injective antihomorphism , considered by Lepowsky in [12], when Go is isomorphic to the rank 1 real form F of the exceptional Lie group F4.
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