Admissible vectors for mock metaplectic representations

Metaplectic Forms and Representations

where the image of A is in the center of G̃. If G and G̃ are topological groups, and if A is a discrete subgroup of the center of G̃, then we may think of G̃ as a cover of G, in the topological sense. So we will sometimes use the term covering group. Very often for us, A will be the group μn(F ) of n-th roots of unity, in a given field F . We will use this notation only if |μn(F )| = n. By a Metapl...

Admissible representations for continuous computations

Admissible Vectors of a Covariant Representation of a Dynamical System

In this paper, we introduce admissible vectors of covariant representations of a dynamical system which are extensions of the usual ones, and compare them with each other. Also, we give some sufficient conditions for a vector to be admissible vector of a covariant pair of a dynamical system.  In addition, we show the existence of Parseval frames for some special subspaces of $L^2(G)$ related to...

Admissible Vectors for the Regular Representation

It is well known that for irreducible, square-integrable representations of a locally compact group, there exist so-called admissible vectors which allow the construction of generalized continuous wavelet transforms. In this paper we discuss when the irreducibility requirement can be dropped, using a connection between generalized wavelet transforms and Plancherel theory. For unimodular groups ...

Principal Series Representations of Metaplectic Groups

We study the principal series representations of central extensions of a split reductive algebraic group by a cyclic group of order n. We compute the Plancherel measure of the representation using Eisenstein series and a comparison method. In addition, we construct genuine central characters of the metaplectic torus in the simply-laced case.