Journal of Lie Theory

no. 1
The Image of the Lepowsky Homomorphism for SO(n,1) and SU(n,1)
Journal of Lie Theory, Volume 21 (2011) no. 1, pp. 165-188
\def\a{{\frak a}} \def\g{{\frak g}} \def\k{{\frak k}} \def\n{{\frak n}} Let $G_o$ be a classical rank one semisimple Lie group and let $K_o$ denote a maximal compact subgroup of $G_o$. Let $U(\g)$ be the complex universal enveloping algebra of $G_o$ and let $U (\g)^K$ denote the centralizer of $K_o$ in $U(\g)$. Also let $P:U(\g)\longrightarrow U(\k)\otimes U(\a)$ be the projection map corresponding to the direct sum $U(\g) = \bigl(U(\k)\otimes U(\a)\bigr)\oplus U(\g)\n$ associated to an Iwasawa decomposition of $G_o$ adapted to $K_o$. In this paper we give a characterization of the image of $U(\g)^K$ under the injective antihomorphism $P:U(\g)^K\longrightarrow U(\k)^M\otimes U(\a)$ when $G_o$ is locally isomorphic to SO$(n,1)$ and SU$(n,1)$.
DOI: 10.5802/jolt.628
Classification: 22E46, 16S30, 16U70
Keywords: Semisimple Lie groups, universal enveloping algebra, representation theory, group invariants, restriction theorem, Kostant degree 
@article{JOLT_2011_21_1_a7,
     author = {A. Brega and L. Cagliero and J. Tirao},
     title = {The {Image} of the {Lepowsky} {Homomorphism} for {SO(n,1)} and {SU(n,1)}},
     journal = {Journal of Lie Theory},
     pages = {165--188},
     year = {2011},
     volume = {21},
     number = {1},
     doi = {10.5802/jolt.628},
     zbl = {1246.22015},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.628/}
}
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A. Brega; L. Cagliero; J. Tirao. The Image of the Lepowsky Homomorphism for SO(n,1) and SU(n,1). Journal of Lie Theory, Volume 21 (2011) no. 1, pp. 165-188. doi: 10.5802/jolt.628

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