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

Destrempes, F.; Pianzola, A.

doi:10.1090/S0002-9939-1994-1185259-5

On a counting formula of Djoković for elements of finite order in compact Lie groups
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by F. Destrempes and A. Pianzola PDF

Proc. Amer. Math. Soc. 121 (1994), 943-950 Request permission

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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