2024/05/25 by Meng-Kiat Chuah, Chuah, Meng-Kiat, R. Fioresi +1
Mathematics · #17B15 #17B20 #53D20 #53D50 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2405.16251
openalex publication_date 2024/05/25 · openalex created_date 2024/05/29 · openalex updated_date 2026/07/28
Geometric quantization transforms a symplectic manifold with Lie group action to a unitary representation. In this article, we extend geometric quantization to the super setting. We consider real forms of contragredient Lie supergroups with compact Cartan subgroups, and study their actions on some pseudo-Kähler supermanifolds. We construct their unitary representations in terms of sections of some line bundles. These unitary representations contain highest weight Harish-Chandra supermodules, whose occurrences depend on the image of the moment map. As a result, we construct a Gelfand model of highest weight Harish-Chandra supermodules. We also perform symplectic reduction, and show that quantization commutes with reduction.