2016/01/31 by Patrick Brosnan, P. Brosnan, Gregory Pearlstein +6 · 2 citations
Engineering · Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Finite Group Theory Research #Mathematics and Applications #Representation Theory (math.RT) #graph theory and CDMA systems #math.AG #math.RT
paper · pdf · doi:10.48550/arxiv.1602.00249
arxiv created 2016/01/31 · openalex publication_date 2016/01/31 · arxiv updated 2016/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe two approaches to classifying the possible monodromy cones C arising from nilpotent orbits in Hodge theory. The first is based upon the observation that C is contained in the open orbit of any interior point N in C under an associated Levi subgroup determined by the limit mixed Hodge structure. The possible relations between the interior of C its faces are described in terms of signed Young diagrams. The second approach is to understand the Tannakian category of nilpotent orbits via a category D introduced by Deligne in a letter to Cattani and Kaplan. In analogy with Hodge theory, there is a functor from D to a subcategory of SL(2)-orbits. We prove that these fibers are, roughly speaking, algebraic. We also give a correction to a result of K. Kato.