Characters of some unitary highest weight representations via the theta correspondence

Abstract

In this article, we consider a dual pair $(G,G^{\prime })$ in the symplectic group $Sp(W)$ with $G$ compact and let $(\tilde{G},{\tilde{G}}^{\prime })$ be the preimages of $G$ and $G^{\prime }$ in the metaplectic group $\widetilde{Sp(W)}$. For every irreducible representation $\Pi$ of $\tilde{G}$ appearing in Howe correspondence, we compute explicitly the restriction of the character ${\Theta }_{{\Pi }^{\prime }}$ of the associated representation ${\Pi }^{\prime }$ of ${\tilde{G}}^{\prime }$ on the set of regular points on the compact Cartan subgroup ${\tilde{H}}^{\prime }$ of ${\tilde{G}}^{\prime }$.

arXiv comment53 pages

References in corpus (1)

• Weyl calculus and dual pairs

Cited by in corpus (2)

• Symmetry breaking operators for dual pairs with one member compact
• Characters of irreducible unitary representations of $U(n,n+1)$ via double lifting from $U(1)$