Characters of some unitary highest weight representations via the theta correspondence
A Merino - Journal of Functional Analysis, 2020 - Elsevier
Journal of Functional Analysis, 2020•Elsevier
In this article, we consider a dual pair (G, G′) in the symplectic group Sp (W) with G
compact and let (G˜, G˜′) be the preimages of G and G′ in the metaplectic group Sp (W)˜.
For every irreducible representation Π of G˜ appearing in Howe correspondence, we
compute explicitly the restriction of the character Θ Π′ of the associated representation Π′
of G˜′ on the set of regular points on the compact Cartan subgroup H˜′ of G˜′.
compact and let (G˜, G˜′) be the preimages of G and G′ in the metaplectic group Sp (W)˜.
For every irreducible representation Π of G˜ appearing in Howe correspondence, we
compute explicitly the restriction of the character Θ Π′ of the associated representation Π′
of G˜′ on the set of regular points on the compact Cartan subgroup H˜′ of G˜′.
In this article, we consider a dual pair (G, G′) in the symplectic group Sp (W) with G compact and let (G˜, G˜′) be the preimages of G and G′ in the metaplectic group Sp (W)˜. For every irreducible representation Π of G˜ appearing in Howe correspondence, we compute explicitly the restriction of the character Θ Π′ of the associated representation Π′ of G˜′ on the set of regular points on the compact Cartan subgroup H˜′ of G˜′.
Elsevier
