Reference : Centralizers of irreducible subgroups in the projective special linear group
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Centralizers of irreducible subgroups in the projective special linear group
[fr] Commutants de sous-groupes irréductibles dans le groupe projectif
Guerin, Clément mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Journal of Group Theory
Walter de Gruyter GmbH & Co. KG.
Yes (verified by ORBilu)
[en] projective representations ; Centralizers of irreducible representations ; Singular locus of character varieties
[en] In this paper, we classify conjugacy classes of centralizers of irreducible subgroups in $PGL(n,\mathbb{C})$ 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.
University of Luxembourg
Fonds National de la Recherche - FnR

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