scholarly journals The Peter-Weyl Theorem and Generalizations

2015 ◽  
Author(s):  
John Bergan
Keyword(s):  
Weyl Theorem

scholarly journals A Kronecker–Weyl theorem for subsets of abelian groups

2011 ◽  
Vol 226 (6) ◽  
pp. 4776-4795 ◽  
Author(s):  
Dikran Dikranjan ◽  
Dmitri Shakhmatov
Keyword(s):  
Abelian Groups ◽  
Weyl Theorem

The Peter-Weyl theorem for SU(1|1)

2015 ◽  
Vol 7 (4) ◽  
pp. 266-275 ◽  
Author(s):  
C. Carmeli ◽  
R. Fioresi ◽  
S. Kwok
Keyword(s):  
Weyl Theorem

scholarly journals A KRONECKER-WEYL THEOREM MODULO 2

1968 ◽  
Vol 60 (4) ◽  
pp. 1163-1164 ◽  
Author(s):  
W. A. Veech
Keyword(s):  
Weyl Theorem

Groups with Representations of Bounded Degree

1949 ◽  
Vol 1 (1) ◽  
pp. 105-112 ◽  
Author(s):  
Irving Kaplansky
Keyword(s):  
Compact Group ◽  
Group Element ◽  
Unitary Representations ◽  
Bounded Degree ◽  
One Dimensional ◽  
Unit Matrix ◽  
Finite Dimensional ◽  
Weyl Theorem ◽  
Irreducible Unitary Representations ◽  
Complete Set

Let G be a compact group. According to the celebrated theorem of Peter-Weyl there exists a complete set of finite-dimensional irreducible unitary representations of G, the completeness meaning that for any group element other than the identity there is a representation sending it into a matrix other than the unit matrix. If G is commutative, the representations are necessarily one-dimensional. It is an immediate consequence of the Peter-Weyl theorem that the converse also holds: if every representation is one-dimensional, G is commutative. The main theorem in the present paper is a generalization of this result to the case where the representations have bounded degree.

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