On conjugacy classes of elements of finite order in compact or complex semisimple Lie groups
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- by Dragomir Ž. Djoković PDF
- Proc. Amer. Math. Soc. 80 (1980), 181-184 Request permission
Abstract:
If K is a connected compact Lie group with simple Lie algebra and if k is an integer relatively prime to the order of the Weyl group W of K then the number $\nu (K,k)$ of conjugacy classes of K consisting of elements x satisfying ${x^k} = 1$ is given by \[ \nu (K,k) = \prod \limits _{i = 1}^l {\frac {{{m_i} + k}}{{{m_i} + 1}},} \] where l is the rank of K and ${m_1}, \ldots ,{m_l}$ are the exponents of W. If G is the complexification of K then we have $\nu (G,k) = \nu (K,k)$ without any restriction on k.References
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Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 80 (1980), 181-184
- MSC: Primary 20G20; Secondary 22E10
- DOI: https://doi.org/10.1090/S0002-9939-1980-0574532-7
- MathSciNet review: 574532