Regular irreducible representations of classical groups over finite quotient rings

2021 ◽  
Vol 311 (1) ◽  
pp. 221-256
Author(s):  
Koichi Takase
Keyword(s):  
Irreducible Representations ◽  
Classical Groups ◽  
Finite Quotient ◽  
Quotient Rings

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).

On the Branching Theorem of the Symplectic Groups

1974 ◽  
Vol 17 (4) ◽  
pp. 535-545 ◽  
Author(s):  
C. Y. Lee
Keyword(s):  
Topological Group ◽  
Differential Equations ◽  
Irreducible Representations ◽  
Symplectic Groups ◽  
Classical Groups ◽  
System Of Differential Equations ◽  
Dominant Weight ◽  
Polynomial Solutions ◽  
Gauss Decomposition ◽  
Representation Spaces

In [1], Zhelobenko introduced the concept of a Gauss decomposition ZtDZ of a topological group and gave characterizations of irreducible representations of the classical groups. In this setting, vectors of representation spaces are polynomial solutions of a system of differential equations and the problem of obtaining branching theorem with respect to a subgroup G0 is to find all polynomial solutions that are invariant under Z ∩ G0 and have dominant weight with respect to D ∩ G0

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