In this paper, we construct a splitting of the metaplectic cover of the reductive 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 result concerning the splitting that we construct and the theta dichotomy for unitary group. The spl...

We obtain explicit formulas for the product of a deformed Weyl denominator with the character of an irreducible representation of the spin group Spin2r+1(C), which is an analogue of the formulas of Tokuyama for Schur polynomials and Hamel-King for characters of symplectic groups. To give these, we start with a symplectic group and obtain such characters using the Casselman-Shalika formula. We t...

We provide formulas for various bases of spherical Whittaker functions on the n-fold metaplectic cover of GLr over a p-adic field and show that there is a basis of symmetric functions in the complex parameter. In addition we relate a specific spherical Whittaker function to the p-power part of the Weyl group multiple Dirichlet series for the root system of type Ar−1 constructed from nth order G...

Let ̃ SL(2, F) be the metaplectic two-fold cover of SL(2, F), the special linear group in two variables over a local field F of characteristic 0. The inverse image T̃ of a maximal torus T in ̃ SL(2, F) is an abelian extension of T by ±1. We consider the question of whether this extension is trivial. More generally we find the minimal subgroup A of the circle for which the extension is split when c...

We consider the action of H = O(p, q) on the matrix space Mp+q,n(R). We study a certain orbit O of H in the null cone N ⊆ Mp+q,n(R) which supports an eigendistribution dνO for H . Using some identities of Capelli type developed in the Appendix, we determine the structure of G̃ = Sp(2n,R)∼-cyclic module generated by dνO under the oscillator representation of G̃ (the metaplectic cover of G = Sp(2n(...

Introduction Let ̃ SL(2,F) be the metaplectic two-fold cover of SL(2,F), the special linear group in two variables over a local field F of characteristic 0. The inverse image T̃ of a maximal torus T in ̃ SL(2,F) is an abelian extension of T by ±1. We consider the question of whether this extension is trivial. We exclude the case F = C, which is trivial. More generally suppose A is a subgroup of th...

M. Hanzer and I. Matić have proved that the genuine unitary principal series representations of the metaplectic groups are irreducible. A simple consequence of that paper is a criterion for the irreducibility of the non-unitary principal series representations of the metaplectic groups that we give in this paper.

The Segal–Shale–Weil representation associates to a symplectic transformation of the Heisenberg group an intertwining operator, called metaplectic operator. We develop an explicit construction of metaplectic operators for the Heisenberg group H(G) of a finite abelian group G, an important setting in finite time-frequency analysis. Our approach also yields a simple construction for the multivari...