Centralizers of irreducible subgroups in the projective linear group

摘要

In this paper, we classify conjugacy classes of centralizers of irreducible subgroups in PGL(n, C) using alternate modules. When n is square-free, we prove that these conjugacy classes are classified by their isomorphism classes. More generally, we define a finite graph related to this classification whose combinatorial properties are expected to help describe the stratification of the bad locus of some character varieties.