Published in Advances in Pure and Applied Mathematics
Let G be a type 1 connected and simply connected solvable Lie group. The generalized moment map for π in G ^ {\widehat{G}} , the unitary dual of G, sends smooth vectors of the representation space of π to 𝒰 ( 𝔤 ) * {{\mathcal{U}(\mathfrak{g})}^{*}} , the dual vector space of 𝒰 ( 𝔤 ) {\mathcal{U}(\mathfrak{g})} . The convex hull of the image of ...
Published in Advances in Pure and Applied Mathematics
So far, the uncertainty principles for solvable non-exponential Lie groups have been treated only in few cases. The first author and Kaniuth produced an analogue of Hardy's theorem for a diamond Lie group, which is a semi-direct product of ℝd with the Heisenberg group ℍ 2d+1 ${\mathbb {H}_{2d+1}}$ In this setting, we formulate and prove in this pap...
Published in Advances in Pure and Applied Mathematics
Let ℍ2n+1r be the reduced Heisenberg Lie group, G = ℍ2n+1r × ℍ2n+1r be the (4n + 2)-dimensional Lie group and ΔG = {(x,x) ∈ G : x ∈ ℍ2n+1r} be the diagonal subgroup of G. Given any discontinuous subgroup Γ ⊂ G for G/ΔG, we provide a layering of the parameter space ℛ(Γ, G, ΔG), which is shown to be endowed with a smooth manifold structure, we also s...
