Journal of Lie Theory

no. 4
Transfer of Characters in the Theta Correspondence with One Compact Member
Journal of Lie Theory, Volume 30 (2020) no. 4, pp. 997-1026
\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 $G'$.
DOI: 10.5802/jolt.1148
Classification: 22E45, 22E46, 22E30
Keywords: Howe correspondence, characters, oscillator semigroup, reductive dual pairs 
@article{JOLT_2020_30_4_a5,
     author = {A. 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},
     doi = {10.5802/jolt.1148},
     zbl = {1475.22020},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1148/}
}
TY  - JOUR
AU  - A. Merino
TI  - Transfer of Characters in the Theta Correspondence with One Compact Member
JO  - Journal of Lie Theory
PY  - 2020
SP  - 997
EP  - 1026
VL  - 30
IS  - 4
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.1148/
DO  - 10.5802/jolt.1148
ID  - JOLT_2020_30_4_a5
ER  - 
%0 Journal Article
%A A. Merino
%T Transfer of Characters in the Theta Correspondence with One Compact Member
%J Journal of Lie Theory
%D 2020
%P 997-1026
%V 30
%N 4
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.1148/
%R 10.5802/jolt.1148
%F JOLT_2020_30_4_a5
A. Merino. Transfer of Characters in the Theta Correspondence with One Compact Member. Journal of Lie Theory, Volume 30 (2020) no. 4, pp. 997-1026. doi: 10.5802/jolt.1148

Cited by Sources: