2010/02/25 by Ishai Dan-Cohen, Ishai Dan‐Cohen, Dan-Cohen, Ishai
Mathematics · #14D23 #14L30 #17B30 #20G05 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.AG #math.RT #msc:14D23 #msc:14L30 #msc:17B30 #msc:20G05
paper · pdf · doi:10.48550/arxiv.1002.4799
78 pages
arxiv created 2010/02/25 · openalex publication_date 2010/02/25 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
With this work we initiate a study of the representations of a unipotent group over a field of characteristic zero from the modular point of view. Let G be such a group. The stack of all representations of a fixed finite dimension n is badly behaved. We introduce an invariant, w, of G, its width, as well as a certain nondegeneracy condition on representations, and we prove that nondegenrate representations of dimension n ≤ w+1 form a quasi-projective variety. Our definition of the width is opaque; as a first attempt to elucidate its behavior, we prove that it is bounded by the length of a composition series. Finally, we study the problem of gluing a pair of nondegenerate representations along a common subquotient.