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arXiv · 1609.06893

Centralizers of irreducible subgroups in the projective special linear group

Clément Guérin
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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.

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Clément Guérin. 2016-09-22. Centralizers of irreducible subgroups in the projective special linear group. https://arxiv.org/abs/1609.06893

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