Geodesic
Transfer of Characters in the Theta Correspondence with One Compact Member
Allan Merino1
1Dept. of Mathematics, National University of Singapore, Singapore 119076
Journal of Lie Theory, Tome 30 (2020) no. 4, pp. 997-1026

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

\newcommand{\Sp}{\textrm{Sp}\,} For an irreducible dual pair $(G, G') \subseteq \Sp(W)$ with one member compact and two representations $\Pi \leftrightarrow \Pi'$ appearing in the Howe duality, we give an expression of the character $\Theta_{\Pi'}$ of $\Pi'$ via the character of $\Pi$. We compute the value of $\Theta_{\Pi'}$ on the maximal compact torus $T'$ of $G'$ for the dual pair $(G = U(n, \mathbb{C}),\, G' = U(p, q, \mathbb{C}))$, which are explicit in low dimensions. For $(G = U(1, \mathbb{C}),\, G' = U(1, 1, \mathbb{C}))$, we determine the value of the character on both Cartan subgroups of $G'$.
Classification : 22E45, 22E46, 22E30
Mots-clés : Howe correspondence, characters, oscillator semigroup, reductive dual pairs

Allan Merino  1

1 Dept. of Mathematics, National University of Singapore, Singapore 119076 
Allan Merino. Transfer of Characters in the Theta Correspondence with One Compact Member. Journal of Lie Theory, Tome 30 (2020) no. 4, pp. 997-1026. http://geodesic.mathdoc.fr/item/JOLT_2020_30_4_a5/
@article{JOLT_2020_30_4_a5,
     author = {Allan Merino},
     title = {Transfer of {Characters} in the {Theta} {Correspondence} with {One} {Compact} {Member}},
     journal = {Journal of Lie Theory},
     pages = {997--1026},
     year = {2020},
     volume = {30},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2020_30_4_a5/}
}
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