On classification of \(\sigma_q\)-conjugacy classes of a loop group. (English) Zbl 1339.22010
It is shown that, for \(q\) not a root of unity, the classification of \(\sigma_q\)-conjugacy classes in a loop group associated to a connected reductive group over a field whose characteristic does not divide the order of the corresponding Weyl group can be reduced to the classification of unipotent classes of, in general not connected, reductive groups. This is applied to recover the classification of \(\sigma_q\)-conjugacy classes in \(\mathrm{GL}_n\).
Reviewer: Volodymyr Mazorchuk (Uppsala)
MSC:
| 22E67 | Loop groups and related constructions, group-theoretic treatment |
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