On the Cortex of the Groups 𝕋n ⋉ ℍn

Abstract

Let [Formula: see text] be the [Formula: see text]-dimensional Heisenberg group and let [Formula: see text] be the [Formula: see text]-dimensional torus acting on [Formula: see text] by automorphisms. We consider the semidirect product group [Formula: see text] The cortex, [Formula: see text] of [Formula: see text] is the set of all unitary irreducible representations [Formula: see text] in the unitary dual [Formula: see text] of [Formula: see text] that cannot be Hausdorff separated from the identity representation [Formula: see text] of [Formula: see text] In this paper, we describe explicitly the cortex ([Formula: see text]) of [Formula: see text] using the coadjoint orbits of the group.