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Correspondence between representations of the dual reductive pair \(O(n)\) and \(\text{SL}_2\). (English) Zbl 0908.20035

Summary: We state a connection between the Weyl representations of the dual reductive pair \(O(n)\) and \(SL_2\), and prove that they have eigenvectors in common.

MSC:

20G05 Representation theory for linear algebraic groups
20G40 Linear algebraic groups over finite fields
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