Splittings of the metaplectic covers of some reductive dual pairs

Authors
Citation
Sy. Pan, Splittings of the metaplectic covers of some reductive dual pairs, PAC J MATH, 199(1), 2001, pp. 163-226
Citations number
14
Categorie Soggetti
Mathematics
Journal title
PACIFIC JOURNAL OF MATHEMATICS
ISSN journal
00308730 → ACNP
Volume
199
Issue
1
Year of publication
2001
Pages
163 - 226
Database
ISI
SICI code
0030-8730(200105)199:1<163:SOTMCO>2.0.ZU;2-8
Abstract
In this paper, we construct a splitting of the metaplectic cover of the red uctive dual pairs of orthogonal and symplectic groups or the reductive dual pairs of unitary groups over a nonarchimedean local field with respect to a generalized lattice model of the Weil representation. We also prove a res ult concerning the splitting that we construct and the theta dichotomy for unitary group. The splitting plays a very crucial role in the study of thet a correspondence for p-adic and finite reductive dual pairs.