Journal of Lie Theory 27 (2017), No. 3, 657--670
Copyright Heldermann Verlag 2017
Local Coefficient Matrices and the Metaplectic Correspondence
Mark Budden
Dept. of Mathematics and Computer Science, Western Carolina University, Cullowhee, NC 28723, U.S.A.
mrbudden@wcu.edu
Geoff Goehle
Dept. of Mathematics and Computer Science, Western Carolina University, Cullowhee, NC 28723, U.S.A.
grgoehle@wcu.edu
The local coefficients of a principal series representation of a metaplectic group are defined in terms of the action of the standard intertwining operator on a canonical basis of the space of Whittaker functionals. By analyzing the nonsingularity of local coefficient matrices, we prove that for a certain class of unramified principal series representations of the metaplectic group, the local metaplectic correspondence preserves irreducibility.
Keywords: Principal series, automorphic forms, Shimura's correspondence.
MSC: 22D30, 11F32; 11F70, 11F85
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