Centralizers of irreducible subgroups in the projective special linear group

Abstract

In this paper, we classify conjugacy classes of centralizers of irreducible subgroups in $PSL(n,\mathbb{C})$ using alternate modules a.k.a. finite abelian groups with an alternate bilinear form. When $n$ is squarefree, 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 us describe the stratification of the singular (orbifold) locus in some character varieties.

32 pages

References in corpus (2)

• Homotopy Groups of Free Group Character Varieties
• Alternate modules are subsymplectic