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Statements

Subject Item
dbr:Mirabolic_group
rdf:type
yago:Abstraction100002137 dbo:EthnicGroup yago:WikicatAlgebraicGroups yago:Group100031264
rdfs:label
Mirabolic group
rdfs:comment
In mathematics, a mirabolic subgroup of the general linear group GLn(k) is a subgroup consisting of automorphisms fixing a given non-zero vector in kn. Mirabolic subgroups were introduced by. The image of a mirabolic subgroup in the projective general linear group is a parabolic subgroup consisting of all elements fixing a given point of projective space. The word "mirabolic" is a portmanteau of "miraculous parabolic". As an algebraic group, a mirabolic subgroup is the semidirect product of a vector space with its group of automorphisms, and such groups are called mirabolic groups. The mirabolic subgroup is used to define the Kirillov model of a representation of the general linear group.
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dbc:Linear_algebraic_groups
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32086828
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1021989386
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dbc:Linear_algebraic_groups dbr:Field_(mathematics) dbr:Parabolic_subgroup dbr:Kirillov_model dbr:Springer-Verlag dbr:Portmanteau dbr:Projective_general_linear_group dbr:General_linear_group
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dbp:bot
medic
dbp:date
May 2021
dbo:abstract
In mathematics, a mirabolic subgroup of the general linear group GLn(k) is a subgroup consisting of automorphisms fixing a given non-zero vector in kn. Mirabolic subgroups were introduced by. The image of a mirabolic subgroup in the projective general linear group is a parabolic subgroup consisting of all elements fixing a given point of projective space. The word "mirabolic" is a portmanteau of "miraculous parabolic". As an algebraic group, a mirabolic subgroup is the semidirect product of a vector space with its group of automorphisms, and such groups are called mirabolic groups. The mirabolic subgroup is used to define the Kirillov model of a representation of the general linear group. As an example, the group of all matrices of the form where a is a nonzero element of the field k and b is any element of k is a mirabolic subgroup of the 2-dimensional general linear group.
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dbr:Subgroup
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