Geodesic
Unitary Representations and the Heisenberg Parabolic Subgroup
Hongyu He1
1Dept. of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A.
Journal of Lie Theory, Tome 21 (2011) no. 4, pp. 847-860

Voir la notice de l'article provenant de la source Heldermann Verlag

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

Hongyu He  1

1 Dept. of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A. 
Hongyu He. Unitary Representations and the Heisenberg Parabolic Subgroup. Journal of Lie Theory, Tome 21 (2011) no. 4, pp. 847-860. http://geodesic.mathdoc.fr/item/JOLT_2011_21_4_a5/
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     author = {Hongyu He},
     title = {Unitary {Representations} and the {Heisenberg} {Parabolic} {Subgroup}},
     journal = {Journal of Lie Theory},
     pages = {847--860},
     year = {2011},
     volume = {21},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2011_21_4_a5/}
}
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