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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On a counting formula of Djoković for elements of finite order in compact Lie groups


Authors: F. Destrempes and A. Pianzola
Journal: Proc. Amer. Math. Soc. 121 (1994), 943-950
MSC: Primary 22E40; Secondary 22C05
MathSciNet review: 1185259
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Abstract: Given a compact connected simple Lie group $ \mathfrak{G}$ and a positive integer N relatively prime to the order of the Weyl group we give a counting formula for the number of conjugacy classes of elements x of order N in $ \mathfrak{G}$ with the property that the N-cyclotonic field when viewed as a Galois extension of the field of characters of x has Galois group containing a fixed chosen cyclic group $ \mathcal{G}$. The case $ \mathcal{G} = \{ 1\} $ recovers a formula, due to Djoković, which counts the number of conjugacy classes of elements of order dividing N in $ \mathfrak{G}$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1185259-5
PII: S 0002-9939(1994)1185259-5
Article copyright: © Copyright 1994 American Mathematical Society