A supercharacter theory for the Sylow p-subgroups of the finite symplectic and orthogonal groups

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dc.creatorAndre, Carlos A. M.
dc.creatorNeto, Ana Margarida
dc.date2008-10-21
dc.date2008-10-31
dc.date.accessioned2026-07-07T10:14:04Z
dc.date.available2026-07-07T10:14:04Z
dc.descriptionWe define the superclasses for a classical finite unipotent group $U$ of type $B_{n}(q)$, $C_{n}(q)$, or $D_{n}(q)$, and show that, together with the supercharacters defined in a previous paper, they form a supercharacter theory. In particular, we prove that the supercharacters take a constant value on each superclass, and evaluate this value. As a consequence, we obtain a factorization of any superclass as a product of elementary superclasses. In addition, we also define the space of superclass functions, and prove that it is spanned by the supercharacters. As as consequence, we (re)obtain the decomposition of the regular character as an orthogonal linear combination of supercharacters. Finally, we define the supercharacter table of $U$, and prove various orthogonality relations for supercharacters (similar to the well-known orthogonality relations for irreducible characters).
dc.descriptionReferences added
dc.identifierhttps://arxiv.org/abs/0810.3761
dc.identifierhttp://arxiv.org/abs/0810.3761
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172752
dc.subjectGroup Theory
dc.subjectRepresentation Theory
dc.subject20C15; 20G40
dc.titleA supercharacter theory for the Sylow p-subgroups of the finite symplectic and orthogonal groups
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