Duke Mathematical Journal
- Duke Math. J.
- Volume 125, Number 3 (2004), 415-465.
Theta lifting of unitary lowest weight modules and their associated cycles
We consider a reductive dual pair (G, G') in the stable range with G' the smaller member and of Hermitian symmetric type. We study the theta lifting of (holomorphic) nilpotent K'ℂ-orbits in relation to the theta lifting of unitary lowest weight representations of G'. We determine the associated cycles of all such representations. In particular, we prove that the multiplicity in the associated cycle is preserved under the theta lifting. We also develop a theory for the lifting of covariants arising from double fibrations by affine quotient maps.
Duke Math. J., Volume 125, Number 3 (2004), 415-465.
First available in Project Euclid: 18 November 2004
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 22E46: Semisimple Lie groups and their representations
Secondary: 11F27: Theta series; Weil representation; theta correspondences
Nishiyama, Kyo; Zhu, Chen-Bo. Theta lifting of unitary lowest weight modules and their associated cycles. Duke Math. J. 125 (2004), no. 3, 415--465. doi:10.1215/S0012-7094-04-12531-X. https://projecteuclid.org/euclid.dmj/1100793677