1 December 2004 Theta lifting of unitary lowest weight modules and their associated cycles
Kyo Nishiyama, Chen-Bo Zhu
Duke Math. J. 125(3): 415-465 (1 December 2004). DOI: 10.1215/S0012-7094-04-12531-X

Abstract

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'-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.

Citation

Download Citation

Kyo Nishiyama. Chen-Bo Zhu. "Theta lifting of unitary lowest weight modules and their associated cycles." Duke Math. J. 125 (3) 415 - 465, 1 December 2004. https://doi.org/10.1215/S0012-7094-04-12531-X

Information

Published: 1 December 2004
First available in Project Euclid: 18 November 2004

zbMATH: 1078.22010
MathSciNet: MR2166751
Digital Object Identifier: 10.1215/S0012-7094-04-12531-X

Subjects:
Primary: 22E46
Secondary: 11F27

Rights: Copyright © 2004 Duke University Press

Vol.125 • No. 3 • 1 December 2004
Back to Top