2023/12/01 by Meng-Kiat Chuah, Fabio Gavarini, Chuah, Meng-Kiat +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Geometry and complex manifolds #math.DG #msc:22E45 #msc:32A36 #msc:53C55 #msc:53D50 #msc:58A50
paper · pdf · doi:10.48550/arxiv.2312.00444
24 pages - Submitted. W.r.t. the previous version, the entire paper has been deeply revised: the main results (that had some flaws) have been amended, and the presentation of the torus case and the Euclidean case have been fused together, which makes the presentation shorter
arxiv created 2026/08/01 · arxiv updated 2026/08/04
Let G be a real Abelian Lie supergroup, let M be its complexification. We classify the G-invariant super Kähler forms on M. For the super Kähler forms with Hamiltonian actions, we extend the scheme of geometric quantization to the super setting and construct unitary G-representations. We show that the irreducible representations that occur in these unitary representations are governed by the image of the moment maps of super Kähler forms. As an application, we construct a Gelfand model of G, namely a unitary G-representation in which every unitary irreducible representation occurs exactly once.