Orthogonal linear group-subgroup pairs with the same invariants

Details Orthogonal linear group-subgroup pairs with the same invariants Orthogonal linear group-subgroup pairs with the same invariants

2005-03-15

arxiv.org/abs/math/0503309v1

Mathematics

Representation Theory

27 pages, a part of PhD thesis

Scientific paper

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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