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Representations of metaplectic groups I: epsilon dichotomy and local Langlands correspondence

Part of: Discontinuous groups and automorphic forms Lie groups

Published online by Cambridge University Press:  31 October 2012

Wee Teck Gan  and
Gordan Savin
Wee Teck Gan
Affiliation:
Department of Mathematics, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, 119076, Singapore (email: wgan@math.ucsd.edu)
Gordan Savin
Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA (email: savin@math.utah.edu)
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Abstract

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Using theta correspondence, we classify the irreducible representations of Mp2n in terms of the irreducible representations of SO2n+1 and determine many properties of this classification. This is a local Shimura correspondence which extends the well-known results of Waldspurger for n=1.

Keywords

metaplectic groupstheta correspondenceepsilon dichotomy

MSC classification

Secondary: 11F27: Theta series; Weil representation; theta correspondences 11F70: Representation-theoretic methods; automorphic representations over local and global fields 22E50: Representations of Lie and linear algebraic groups over local fields

Information

Type
Research Article
Information
Compositio Mathematica , Volume 148 , Issue 6 , November 2012 , pp. 1655 - 1694
Copyright
Copyright © Foundation Compositio Mathematica 2012

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