2010/09/18 by Ajneet Dhillon, Sheldon Joyner
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Cover (algebra) #Functor #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematics #Pullback #Pure mathematics #Representation (politics) #Tensor (intrinsic definition) #Tensor field #Vector bundle #math.AG #msc:14H60
paper · pdf · doi:10.1307/mmj/1331222855
published as Mich Math J, Vol 61 no 1 (2012), 199-224 · 25 pages
arxiv created 2010/09/18 · openalex publication_date 2012/03/01 · arxiv updated 2012/08/09 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/15
We work over an algebraically closed ground field of characteristic zero. A G-cover of \mathbb P1 ramified at three points allows one to assign to each finite dimensional representation V of G a vector bundle ⊕ \mathscrO(si) on \mathbb P1 with parabolic structure at the ramification points. This produces a tensor functor from representation of G to vector bundles with parabolic structure that characterises the original cover. This work attempts to describe this tensor functor in terms of group theoretic data. More precisely, we construct a pullback functor on vector bundles with parabolic structure and describe the parabolic pullback of the previously described tensor functor.