Local coefficient matrices and the metaplectic correspondence

The local coefficients of a principal series representation of a metaplectic group G̃ 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.