On local Whittaker models for the Jacobi group of degree one (Q1340232)

The author studies the representation theory of the Jacobi group \(G^J\) of degree 1 over a local field \(F\), i.e. the semidirect product of the group \(\text{SL}_2 (F)\) with a Heisenberg group. In particular he addresses the question of existence and uniqueness of Whittaker models for unitary irreducible representations of this group. Existence and uniqueness are shown for the restriction of the functional to a certain subspace of the representation space (subject to some additional constraints on the representation studied). The main tool is the decomposition of the representation of \(G^J\) into the tensor product of the Weil representation of \(G^J\) and a representation of the metaplectic group. An alternative approach using differential equations is also discussed.