The Image of the Lepowsky Homomorphism for the Group F_4^{-20}

O. BREGA; L. CAGLIERO; J. TIRAO

INTERNATIONAL MATHEMATICS RESEARCH NOTICES

OXFORD UNIV PRESS

Lugar: Oxford; Año: 2012 p. 1 - 34

1073-7928

Let Go be a semisimple Lie group, let Ko be a maximal compact subgroup of Go and let g, k denote the complexification of their Lie algebras. Let G be the adjoint group of g and let K be the connected Lie subgroup of G with Lie algebra k. If U(g) is the universal enveloping algebra of g, then will denote U(g)^K the centralizer of K in U(g). Also let P be the projection map corresponding to the direct sum g = k + a + 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, when Go is isomorphic to the rank 1 real form F_1^20 of the exceptional Lie group F4.