The minimal polynomials of unipotent elements in irreducible representations of the classical groups in odd characteristic

2009 ◽  
Vol 200 (939) ◽  
pp. 0-0 ◽  
Author(s):  
I. D. Suprunenko
Keyword(s):  
Irreducible Representations ◽  
Classical Groups ◽  
Minimal Polynomials

Representations and automorphisms of some wreath products

1979 ◽  
Vol 85 (1) ◽  
pp. 49-53 ◽  
Author(s):  
Roderick Gow
Keyword(s):  
Automorphism Groups ◽  
Wreath Products ◽  
Irreducible Representations ◽  
Classical Groups

In this paper we study the faithful irreducible representations of certain families of wreath products and show how a particular class of such representations is related to the automorphisms of these groups. Our methods enable us to calculate the orders of the automorphism groups, although they do not deal with their structure. The wreath products that we consider here include most of the Sylow p-subgroups of the classical groups, which are described in (1) and (4).

scholarly journals The minimal polynomials of powers of cycles in the ordinary representations of symmetric and alternating groups

2020 ◽  
pp. 2150209
Author(s):  
Nanying Yang ◽  
Alexey M. Staroletov
Keyword(s):  
Symmetric Groups ◽  
Irreducible Representations ◽  
Alternating Groups ◽  
Minimal Polynomials ◽  
Alternating And Symmetric Groups

Denote the alternating and symmetric groups of degree [Formula: see text] by [Formula: see text] and [Formula: see text], respectively. Consider a permutation [Formula: see text], all of whose nontrivial cycles are of the same length. We find the minimal polynomials of [Formula: see text] in the ordinary irreducible representations of [Formula: see text] and [Formula: see text].

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