1987/01/01 by James E. Humphreys · 3 citations
Computer Science · Mathematics · #Topological and Geometric Data Analysis #Mathematics
paper · pdf · doi:10.1090/s0273-0979-1987-15512-1
openalex publication_date 1987/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/07
Introduction. Group representations occupy a sort of middle ground between abstract groups and transformation groups, i.e., groups acting in concrete ways as permutations of sets, homeomorphisms of topological spaces, diffeomorphisms of manifolds, etc. The requirement that the elements of a group act as linear operators on a vector space limits somewhat the complexity of the action without sacrificing the depth or applicability of the resulting theory. As in other areas of mathematics, study of linear phenomena may illuminate more general phenomena.