Uniqueness of Whittaker functionals on the metaplectic group (Q1804667)

This paper deals with a question which arises in the theory of metaplectic extensions of \(GL (r)\) over a local field \(F\). We suppose that the local field contains the \(n\)-th roots of unity. Then Kazhdan and Patterson proved that there are certain exceptional representations of the metaplectic group which have unique Whittaker models when \(r=n\) or \(n-1\). In fact the case \(r=n\) arises as a subquotient of an induced representation based on an exceptional representation in the case \(r= n- 1\). In this paper the authors prove directly that the induced representation itself has a unique Whittaker model.