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Linear representation theory of symmetric group:S3

64 bytes added, 02:20, 5 December 2011
Family contexts
! Family name !! Parameter values !! General discussion of linear representation theory of family !! Section in this article !! Comparative note
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| [[symmetric group]] || 3 || [[Family version::linear representation theory of symmetric groups]] || [[#Interpretation as symmetric group]] || For any symmetric group on a finite set, all irreducible linear representations can be realized with entries in <math>\mathbb{Z}</math>, and these give irreducible representations over any field of characteristic not dividing the order of the group.
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| [[dihedral group]] || 3 || [[Family version::linear representation theory of dihedral groups]] || [[#Interpretation as dihedral group]] || For a dihedral group, the irreducible representations can be realized in a finite extension of <math>\mathbb{Z}</math> but not in <math>\mathbb{Z}</matH> itself except for degrees 3,4,6 (orders 6,8,12).
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| [[general affine group of degree one]] || [[field:F3]] || [[Family version::linear representation theory of general affine group of degree one over a finite field]] || [[#Interpretation as general affine group of degree one]] ||
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| [[general linear group of degree two]] || [[field:F2]] || [[Family version::linear representation theory of general linear group of degree two over a finite field]] || [[#Interpretation as general linear group of degree two]] ||
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