Geodesic
Unitary Representations and the Heisenberg Parabolic Subgroup
Journal of Lie theory, Tome 21 (2011) no. 4, pp. 847-86 Cet article a éte moissonné depuis la source Heldermann Verlag

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We study the restriction of an irreducible unitary representation $\pi$ of the universal covering $\widetilde{Sp}_{2n}(\R)$ to a Heisenberg maximal parabolic subgroup $\tilde P$. We prove that if $\pi|_{\tilde P}$ is irreducible, then $\pi$ must be a highest weight module or a lowest weight module. This is in sharp contrast with the GL$_n(\R)$ case. In addition, we show that for a unitary highest or lowest weight module, $\pi|_{\tilde P}$ decomposes discretely. We also treat the groups $U(p,q)$ and $O^*(2n)$.
Classification : 22E45, 43A80
Mots-clés : Parabolic subgroups, Heisenberg group, Mackey analysis, branching formula, unitary representations, Kirillov Conjecture, symplectic group, highest weight module 
@article{JLT_2011_21_4_JLT_2011_21_4_a5,
     author = {H. He },
     title = {Unitary {Representations} and the {Heisenberg} {Parabolic} {Subgroup}},
     journal = {Journal of Lie theory},
     pages = {847--86},
     year = {2011},
     volume = {21},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2011_21_4_JLT_2011_21_4_a5/}
}
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H. He . Unitary Representations and the Heisenberg Parabolic Subgroup. Journal of Lie theory, Tome 21 (2011) no. 4, pp. 847-86. http://geodesic.mathdoc.fr/item/JLT_2011_21_4_JLT_2011_21_4_a5/