Holomorphic current groups -- Structure and Orbits

2014/08/18 by Martin Laubinger, Laubinger, Martin, Friedrich Wagemann +1
Mathematics · Physics and Astronomy · #20F28 #22E65 #22E67 #32A38 #46G20 #58D15 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AT #math.CV #math.DG #math.MP #msc:20F28 #msc:22E65 #msc:22E67 #msc:32A38 #msc:46G20 #msc:58D15

paper · pdf · doi:10.48550/arxiv.1408.3990

28 pages

arxiv created 2014/08/18 · openalex publication_date 2014/08/18 · arxiv updated 2014/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be a finite-dimensional, 1-connected complex Lie group, and let Σ_k=Σ- p₁,…,p_k\ be a compact connected Riemann surface Σ, from which we have extracted k > 0 distinct points. We study in this article the regular Frechet-Lie group O(Σ_k,K) of holomorphic maps from Σ_k to K and its central extension \widehatO(Σ_k,K). We feature especially the automorphism groups of these Lie groups as well as the coadjoint orbits of \widehatO(Σ_k,K) which we link to flat K-bundles on Σ_k.

Citations

• Complex Structures on Principal Bundles

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