2017/04/01 by Kiran Luecke, Luecke, Kiran
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1704.00089
openalex publication_date 2017/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper I present a new and unified method of proving character formulas for discrete series representations of connected Lie groups by applying a Chern character-type construction to the matrix factorizations of [FT] and [FHT3]. In the case of a compact group I recover the Kirillov formula, thereby exhibiting the work of [FT] as a categorification of the Kirillov correspondence. In the case of a real semisimple group I recover the Rossman character formula with only a minimal amount of analysis. The appeal of this method is that it relies almost entirely on highest-weight theory, which is a far more ubiquitous phenomenon than the varied techniques that were previously used to prove such formulas.