Piatetski-Shapiro, Ilya I.; Teicher, Mina Correspondence between representations of the dual reductive pair \(O(n)\) and \(\text{SL}_2\). (English) Zbl 0908.20035 Beitr. Algebra Geom. 38, No. 1, 145-148 (1997). 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 Keywords:Weyl representations; dual reductive pairs PDF BibTeX XML Cite \textit{I. I. Piatetski-Shapiro} and \textit{M. Teicher}, Beitr. Algebra Geom. 38, No. 1, 145--148 (1997; Zbl 0908.20035) Full Text: EuDML EMIS OpenURL