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Orthogonal linear group-subgroup pairs with the same invariants

S. Solomon
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Abstract

The main theorem of Galois theory states that there are no finite group-subgroup pairs with the same invariants. On the other hand, if we consider complex linear reductive groups instead of finite groups, the analogous statement is no longer true: There exist counterexample group-subgroup pairs with the same invariants. However, it's possible to classify all these counterexamples for certain types of groups. In [16], we provided the classification for connected complex irreducible groups, and, in this paper, for connected complex orthogonal groups, i.e., groups that preserve some non-degenerate quadratic form.

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S. Solomon. 2005-03-15. Orthogonal linear group-subgroup pairs with the same invariants. https://arxiv.org/abs/math/0503309

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