Minimal polynomials of elements of order 𝑝 in irreducible representations of Chevalley groups over fields of characteristic 𝑝

1992 ◽  
pp. 389-400
Author(s):  
I. D. Suprunenko
Keyword(s):  
Irreducible Representations ◽  
Chevalley Groups ◽  
Minimal Polynomials

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].

An Intuitive Method for the Determination of Crystal-Field Parameters in Laser Crystals

1993 ◽  
Vol 329 ◽  
Author(s):  
Frederick G. Anderson ◽  
H. Weidner ◽  
P. L. Summers ◽  
R. E. Peale ◽  
B. H. T. Chai
Keyword(s):  
Crystal Field ◽  
Irreducible Representations ◽  
Laser Crystals ◽  
Intuitive Method ◽  
Crystal Field Parameters ◽  
Intuitive Interpretation

AbstractExpanding the crystal field in terms of operators that transform as the irreducible representations of the Td group leads to an intuitive interpretation of the crystal-field parameters. We apply this method to the crystal field experienced by Nd3+ dopants in the laser crystals YLiF4, YVO4, and KLiYF5.

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