Article (Scientific journals)
Centralizers of irreducible subgroups in the projective special linear group
Guerin, Clément
2018In Journal of Group Theory
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Keywords :
projective representations; Centralizers of irreducible representations; Singular locus of character varieties
Abstract :
[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.
Research center :
University of Luxembourg
Disciplines :
Mathematics
Author, co-author :
Guerin, Clément ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
External co-authors :
no
Language :
English
Title :
Centralizers of irreducible subgroups in the projective special linear group
Alternative titles :
[fr] Commutants de sous-groupes irréductibles dans le groupe projectif
Publication date :
June 2018
Journal title :
Journal of Group Theory
ISSN :
1433-5883
Publisher :
Walter de Gruyter GmbH & Co. KG.
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
FNR - Fonds National de la Recherche [LU]
Available on ORBilu :
since 21 December 2016

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